[
{
"id": 6251,
"type": 1,
"question": "How many boats are there?",
"answers": [
"five",
"four",
"six",
"eight"
],
"correct_index": 0,
"solution": "Look at the picture. Count the boats one by one: 1, 2, 3, 4, 5. There are 5 boats.
Final Answer: A: five"
},
{
"id": 6252,
"type": 2,
"question": "There are letters in the word 'chicken'.",
"answers": [
"7",
null,
null,
null
],
"correct_index": 7,
"solution": "Write the word 'chicken' and count each letter: c, h, i, c, k, e, n. That is 7 letters.
Final Answer: 7"
},
{
"id": 6253,
"type": 2,
"question": "In the word 'number', there are letters.",
"answers": [
"6",
null,
null,
null
],
"correct_index": 6,
"solution": "Write the word 'number' and count each letter: n, u, m, b, e, r. That is 6 letters.
Final Answer: 6"
},
{
"id": 6254,
"type": 2,
"question": "The word 'baby' has letters.",
"answers": [
"4",
null,
null,
null
],
"correct_index": 4,
"solution": "Write the word 'baby' and count each letter: b, a, b, y. That is 4 letters.
Final Answer: 4"
},
{
"id": 6283,
"type": 1,
"question": "Count. How many balloons are there?",
"answers": [
"eleven",
"six",
"four",
"seven"
],
"correct_index": 2,
"solution": "Look at the picture. Count the balloons one by one: 1, 2, 3, 4. There are 4 balloons.
Final Answer: C: four"
},
{
"id": 6284,
"type": 1,
"question": "How many?",
"answers": [
"ten",
"twelve",
" two",
"three"
],
"correct_index": 0,
"solution": "Look at the picture. Count the objects one by one from 1 to 10. There are 10 objects.
Final Answer: A: ten"
},
{
"id": 6285,
"type": 1,
"question": "How many?",
"answers": [
"ten",
" four",
" two",
"one"
],
"correct_index": 3,
"solution": "Look at the picture. There is only 1 object shown.
Final Answer: D: one"
},
{
"id": 6286,
"type": 1,
"question": "How many boats are there?",
"answers": [
"five",
"four",
"six",
"eight"
],
"correct_index": 0,
"solution": "Look at the picture. Count the boats one by one: 1, 2, 3, 4, 5. There are 5 boats.
Final Answer: A: five"
},
{
"id": 6287,
"type": 2,
"question": "There are letters in the word 'chicken'.",
"answers": [
"7",
null,
null,
null
],
"correct_index": 7,
"solution": "Write the word 'chicken' and count each letter: c, h, i, c, k, e, n. That is 7 letters.
Final Answer: 7"
},
{
"id": 6288,
"type": 2,
"question": "In the word 'number', there are letters.",
"answers": [
"6",
null,
null,
null
],
"correct_index": 6,
"solution": "Write the word 'number' and count each letter: n, u, m, b, e, r. That is 6 letters.
Final Answer: 6"
},
{
"id": 6289,
"type": 2,
"question": "The word 'baby' has letters.",
"answers": [
"4",
null,
null,
null
],
"correct_index": 4,
"solution": "Write the word 'baby' and count each letter: b, a, b, y. That is 4 letters.
Final Answer: 4"
},
{
"id": 6290,
"type": 2,
"question": "How many apples are there in the basket?",
"answers": [
"3",
"5",
"2",
"4"
],
"correct_index": 0,
"solution": "Count the apples in the basket one by one: 1, 2, 3. There are 3 apples.
Final Answer: 3"
},
{
"id": 6291,
"type": 2,
"question": "Count the number of stars in the sky.",
"answers": [
"7",
"9",
"5",
"8"
],
"correct_index": 1,
"solution": "Count the stars in the sky one by one: 1, 2, 3, 4, 5, 6, 7, 8, 9. There are 9 stars.
Final Answer: 9"
},
{
"id": 6292,
"type": 1,
"question": "How many apples are there?",
"answers": [
"four",
"three",
"two",
"seven"
],
"correct_index": 0,
"solution": "Count the apples shown in the picture.
\nThere are 4 apples.
\nFinal Answer: 4\n"
},
{
"id": 6293,
"type": 1,
"question": "Count the stars in the sky.",
"answers": [
"six",
"four",
"two",
"eight"
],
"correct_index": 1,
"solution": "Count the stars one by one: 1, 2, 3, 4. There are 4 stars.
Final Answer: B: four"
},
{
"id": 6294,
"type": 1,
"question": "How many pencils are on the table?",
"answers": [
"three",
"five",
"two",
"seven"
],
"correct_index": 0,
"solution": "Count the pencils on the table one by one: 1, 2, 3. There are 3 pencils.
Final Answer: A: three"
},
{
"id": 6295,
"type": 1,
"question": "Count the number of flowers in the garden.",
"answers": [
"four",
"six",
"eight",
"two"
],
"correct_index": 1,
"solution": "Count the flowers in the garden one by one: 1, 2, 3, 4, 5, 6. There are 6 flowers.
Final Answer: B: six"
},
{
"id": 6296,
"type": 1,
"question": "How many balls can you see?",
"answers": [
"six",
"three",
"five",
"eight"
],
"correct_index": 2,
"solution": "Count the balls one by one: 1, 2, 3, 4, 5. There are 5 balls.
Final Answer: C: five"
},
{
"id": 6297,
"type": 1,
"question": "Count the number of books on the shelf.",
"answers": [
"two",
"four",
"six",
"eight"
],
"correct_index": 1,
"solution": "Count the books on the shelf one by one: 1, 2, 3, 4. There are 4 books.
Final Answer: B: four"
},
{
"id": 6298,
"type": 1,
"question": "How many ducks are swimming in the pond?",
"answers": [
"five",
"three",
"seven",
"two"
],
"correct_index": 0,
"solution": "Count the ducks in the pond one by one: 1, 2, 3, 4, 5. There are 5 ducks.
Final Answer: A: five"
},
{
"id": 6299,
"type": 1,
"question": "Count the number of trees in the park.",
"answers": [
"eight",
"five",
"three",
"seven"
],
"correct_index": 1,
"solution": "Count the trees in the park one by one: 1, 2, 3, 4, 5. There are 5 trees.
Final Answer: B: five"
},
{
"id": 6300,
"type": 1,
"question": "How many fish are in the aquarium?",
"answers": [
"four",
"six",
"two",
"eight"
],
"correct_index": 0,
"solution": "Count the fish in the aquarium one by one: 1, 2, 3, 4. There are 4 fish.
Final Answer: A: four"
},
{
"id": 6301,
"type": 1,
"question": "Count the number of balloons in the room.",
"answers": [
"three",
"five",
"seven",
"two"
],
"correct_index": 1,
"solution": "Count the balloons in the room one by one: 1, 2, 3, 4, 5. There are 5 balloons.
Final Answer: B: five"
},
{
"id": 6302,
"type": 1,
"question": "Count the number of apples in the basket.",
"answers": [
"5",
"3",
"4",
"2"
],
"correct_index": 2,
"solution": "Count the apples inside the basket one by one.
\nThere are 4 apples in the basket.
\nFinal Answer: 4\n"
},
{
"id": 6303,
"type": 1,
"question": "How many stars are there? ",
"answers": [
"5",
"6",
"2",
"1"
],
"correct_index": 3,
"solution": "Look at the picture and count the stars shown.
\nThere is 1 star.
\nFinal Answer: 1\n"
},
{
"id": 6305,
"type": 1,
"question": "How many apples are there?",
"answers": [
"five",
"three",
"seven",
"two"
],
"correct_index": 1,
"solution": "Count the apples shown in the picture one by one.
\n• The picture shows 3 apples.
\nFinal Answer: B: three\n"
},
{
"id": 6306,
"type": 1,
"question": "Count the number of butterflies.",
"answers": [
"four",
"six",
"two",
"eight"
],
"correct_index": 0,
"solution": "Count the butterflies shown in the picture one by one.
\n• The picture shows 4 butterflies.
\nFinal Answer: A: four\n"
},
{
"id": 6307,
"type": 1,
"question": "How many teddy bears can you see?",
"answers": [
"three",
"one",
"five",
"two"
],
"correct_index": 2,
"solution": "Count the teddy bears shown in the picture one by one.
\n• The picture shows 5 teddy bears.
\nFinal Answer: C: five\n"
},
{
"id": 6308,
"type": 1,
"question": "Determine the total number of balloons. How many balloons are there in total?",
"answers": [
"A) five",
"B) eight",
"C) four",
"D) ten"
],
"correct_index": 2,
"solution": "Count all the balloons shown in the picture one by one.
\n• The picture shows 4 balloons in total.
\nFinal Answer: C: four\n"
},
{
"id": 6309,
"type": 1,
"question": "Count and identify the number of balloons present. How many balloons can you see?",
"answers": [
"A) three",
"B) seven",
"C) four",
"D) nine"
],
"correct_index": 2,
"solution": "Count all the balloons shown in the picture one by one.
\n• The picture shows 4 balloons.
\nFinal Answer: C: four\n"
},
{
"id": 6310,
"type": 1,
"question": "Calculate the total balloons. What is the total count of balloons?",
"answers": [
"A) six",
"B) ten",
"C) four",
"D) eight"
],
"correct_index": 2,
"solution": "Count all the balloons shown in the picture one by one.
\n• The total number of balloons is 4.
\nFinal Answer: C: four\n"
},
{
"id": 6311,
"type": 1,
"question": "How many cats can you see?",
"answers": [
"A) three",
"B) five",
"C) two",
"D) four"
],
"correct_index": 1,
"solution": "Count the cats shown in the picture one by one.
\n• The picture shows 5 cats.
\nFinal Answer: B: five\n"
},
{
"id": 6312,
"type": 1,
"question": "In the picture, how many apples are there?",
"answers": [
"A) six",
"B) three",
"C) five",
"D) two"
],
"correct_index": 2,
"solution": "Count the apples shown in the picture one by one.
\n• The picture shows 5 apples.
\nFinal Answer: C: five\n"
},
{
"id": 6313,
"type": 1,
"question": "Count the number of trees in the park.",
"answers": [
"A) eight",
"B) three",
"C) five",
"D) two"
],
"correct_index": 2,
"solution": "Count the trees shown in the picture one by one.
\n• The picture shows 5 trees in the park.
\nFinal Answer: C: five\n"
},
{
"id": 6314,
"type": 1,
"question": "What is the total number of pencils on the desk?",
"answers": [
"3",
"6",
"2",
"4"
],
"correct_index": 0,
"solution": "Count all the pencils shown on the desk.
\nThere are 3 pencils in total.
\nFinal Answer: 3\n"
},
{
"id": 6315,
"type": 1,
"question": "How many cookies are left in the jar?",
"answers": [
"1",
"5",
"3",
"4"
],
"correct_index": 1,
"solution": "Count the cookies remaining inside the jar.
\nThere are 5 cookies left in the jar.
\nFinal Answer: 5\n"
},
{
"id": 6316,
"type": 1,
"question": "How many letters are in the word 'baby'?",
"answers": [
"3",
"4",
"5",
"6"
],
"correct_index": 1,
"solution": "Count each letter in the word \"baby\".
\n• b-a-b-y: that is 4 letters.
\nFinal Answer: B: 4\n"
},
{
"id": 6317,
"type": 1,
"question": "Count the number of characters in the term 'baby'.",
"answers": [
"3",
"4",
"5",
"6"
],
"correct_index": 1,
"solution": "Count each character in the word \"baby\".
\n• b-a-b-y: that is 4 characters.
\nFinal Answer: B: 4\n"
},
{
"id": 6318,
"type": 1,
"question": "Determine the total letters in 'baby'.",
"answers": [
"3",
"4",
"5",
"6"
],
"correct_index": 1,
"solution": "Count the total number of letters in \"baby\".
\n• b-a-b-y: there are 4 letters.
\nFinal Answer: B: 4\n"
},
{
"id": 6319,
"type": 1,
"question": "How many characters make up the word 'baby'?",
"answers": [
"3",
"4",
"5",
"6"
],
"correct_index": 1,
"solution": "Count the number of characters that make up the word \"baby\".
\n• b-a-b-y: that is 4 characters.
\nFinal Answer: B: 4\n"
},
{
"id": 6320,
"type": 1,
"question": "Calculate the number of letters in the term 'baby'.",
"answers": [
"3",
"4",
"5",
"6"
],
"correct_index": 1,
"solution": "Count the letters in the word \"baby\" one by one.
\n• b-a-b-y: there are 4 letters.
\nFinal Answer: B: 4\n"
},
{
"id": 6321,
"type": 2,
"question": "The word 'apple' has how many letters? Answer: ",
"answers": [
"5",
"",
"",
""
],
"correct_index": 5,
"solution": "Count the letters in the word \"apple\".
\n• a-p-p-l-e: that is 5 letters.
\nFinal Answer: 5\n"
},
{
"id": 6322,
"type": 2,
"question": "How many letters are there in the word 'elephant'?",
"answers": [
"9",
"",
"",
""
],
"correct_index": 8,
"solution": "\nCount each letter in the word 'elephant': e-l-e-p-h-a-n-t.
\nThere are 8 letters.
\nFinal Answer: 8\n"
},
{
"id": 6323,
"type": 2,
"question": "Calculate the number of letters in the term 'sunshine'. Answer: ",
"answers": [
"8",
"",
"",
""
],
"correct_index": 8,
"solution": "Count the letters in the word \"sunshine\".
\n• s-u-n-s-h-i-n-e: that is 8 letters.
\nFinal Answer: 8\n"
},
{
"id": 6324,
"type": 2,
"question": "Convert 500 cm to meters. Answer : m",
"answers": [
"5",
null,
null,
null
],
"correct_index": 1,
"solution": "1 metre (m) = 100 centimetres (cm). To convert cm to m, divide by 100.
• 500 ÷ 100 = 5
Final Answer: 5"
},
{
"id": 6325,
"type": 2,
"question": "Convert 3.5 kg to grams. \nAnswer: g",
"answers": [
null,
null,
"3500",
null
],
"correct_index": 2,
"solution": "1 kg = 1000 g. Multiply the number of kilograms by 1000.
\r\n• 3.5 kg = 3.5 × 1000 = 3500 g
\r\nFinal Answer: 3500\r\n"
},
{
"id": 6326,
"type": 1,
"question": "If a container holds 2.5 liters of water, how many milliliters of water does it contain?",
"answers": [
"2500 ml",
"250 ml",
"25 ml",
"0.25 ml"
],
"correct_index": 0,
"solution": "1 litre = 1000 millilitres. Multiply the number of litres by 1000.
\r\n• 2.5 L = 2.5 × 1000 = 2500 mL
\r\nFinal Answer: A: 2500 ml\r\n"
},
{
"id": 6327,
"type": 1,
"question": "Convert 1.2 meters to centimeters.",
"answers": [
"120 cm",
"1.2 cm",
"12 cm",
"0.12 cm"
],
"correct_index": 0,
"solution": "1 metre = 100 centimetres. Multiply the number of metres by 100.
\r\n• 1.2 m = 1.2 × 100 = 120 cm
\r\nFinal Answer: A: 120 cm\r\n"
},
{
"id": 6328,
"type": 2,
"question": "If a book weighs 0.75 kg, how many grams does it weigh? \nAnswer: g",
"answers": [
"750",
null,
null,
null
],
"correct_index": 0,
"solution": "1 kilogram (kg) = 1000 grams (g). To convert kg to g, multiply by 1000.
• 0.75 × 1000 = 750
Final Answer: 750"
},
{
"id": 6329,
"type": 2,
"question": "A tank contains 4.5 liters of fuel. How many milliliters of fuel does the tank hold? \nAnswer: ml",
"answers": [
"4500",
null,
null,
null
],
"correct_index": 0,
"solution": "1 litre = 1000 millilitres. Multiply the number of litres by 1000.
\r\n• 4.5 L = 4.5 × 1000 = 4500 mL
\r\nFinal Answer: 4500\r\n"
},
{
"id": 6330,
"type": 1,
"question": "Express 600 grams in kilograms.",
"answers": [
"60 kg",
"6 kg",
"0.6 kg",
"0.06 kg"
],
"correct_index": 2,
"solution": "1 kg = 1000 g, so divide by 1000 to convert grams to kilograms.
\r\n• 600 ÷ 1000 = 0.6 \r\n \r\nFinal Answer: 0.6 kg"
},
{
"id": 6331,
"type": 2,
"question": "If a box measures 240 cm in length, what is the length of the box in meters? \nAnswer: m",
"answers": [
"2.4",
null,
null,
null
],
"correct_index": 0,
"solution": "1 metre = 100 centimetres. To convert centimetres to metres, divide by 100.
\r\n• 240 cm = 240 ÷ 100 = 2.4 m
\r\nFinal Answer: 2.4\r\n"
},
{
"id": 6332,
"type": 2,
"question": "Convert 2.8 kilograms to grams. Amswer: g",
"answers": [
"2800",
null,
null,
null
],
"correct_index": 0,
"solution": "1 kg = 1000 g. Multiply the number of kilograms by 1000.
\r\n• 2.8 kg = 2.8 × 1000 = 2800 g
\r\nFinal Answer: 2800\r\n"
},
{
"id": 6333,
"type": 1,
"question": "If a jug holds 3.6 liters of juice, how many milliliters of juice can it contain?",
"answers": [
"360 ml",
"3600 ml",
"36 ml",
"0.36 ml"
],
"correct_index": 1,
"solution": "1 litre = 1000 millilitres.
\r\n• 3.6 × 1000 = 3600 \r\n \r\nFinal Answer: 3600 ml"
},
{
"id": 6334,
"type": 1,
"question": "How many cats are in the picture?",
"answers": [
"Option A) three",
"Option B) five",
"Option C) two",
"Option D) four"
],
"correct_index": 2,
"solution": "Count the cats shown in the picture.
\nThere are 2 cats, which matches Option C.
\nFinal Answer: Option C: two\n"
},
{
"id": 6335,
"type": 1,
"question": "How many books are on the shelf?",
"answers": [
"Option A) two",
"Option B) five",
"Option C) three",
"Option D) six"
],
"correct_index": 2,
"solution": "Count the books shown on the shelf.
\nThere are 3 books, which matches Option C.
\nFinal Answer: Option C: three\n"
},
{
"id": 6339,
"type": 1,
"question": "How many apples are there?",
"answers": [
"Three",
"Five",
"Two",
"Four"
],
"correct_index": 0,
"solution": "Count the apples in the picture one by one.
• Look carefully at the picture showing the apples. • Count: 1, 2, 3.
There are 3 apples in the picture.
Final Answer: A: Three\n"
},
{
"id": 6340,
"type": 1,
"question": "Count the number of butterflies.",
"answers": [
"Six",
"Two",
"Eight",
"Five"
],
"correct_index": 3,
"solution": "Count the butterflies in the picture one by one.
• Look carefully at the picture showing the butterflies. • Count: 1, 2, 3, 4, 5.
There are 5 butterflies.
Final Answer: D: Five\n"
},
{
"id": 6341,
"type": 1,
"question": "How many pencils are in the box?",
"answers": [
"Ten",
"Eight",
"Six",
"Three"
],
"correct_index": 2,
"solution": "Count the pencils in the box one by one.
• Look carefully at the pencils in the picture. • Count: 1, 2, 3, 4, 5, 6.
There are 6 pencils in the box.
Final Answer: C: Six\n"
},
{
"id": 6342,
"type": 1,
"question": "What is the count of the flowers?",
"answers": [
"Two",
"Three",
"Five",
"Six"
],
"correct_index": 1,
"solution": "Count the flowers in the picture one by one.
• Look carefully at the picture showing the flowers. • Count: 1, 2, 3.
There are 3 flowers.
Final Answer: B: Three\n"
},
{
"id": 6343,
"type": 1,
"question": "How many birds can you see?",
"answers": [
"Four",
"Seven",
"Nine",
"Two"
],
"correct_index": 0,
"solution": "Count the birds in the picture one by one.
• Look carefully at the picture showing the birds. • Count: 1, 2, 3, 4.
There are 4 birds.
Final Answer: A: Four\n"
},
{
"id": 6344,
"type": 2,
"question": "Fill in the blanks: There are pencils.",
"answers": [
"5",
"",
"",
""
],
"correct_index": 0,
"solution": "Count the pencils in the picture one by one.
• Look carefully at the picture. • Count the pencils: 1, 2, 3, 4, 5.
There are 5 pencils.
Final Answer: 5\n"
},
{
"id": 6345,
"type": 2,
"question": "How many cats do you see? ",
"answers": [
"3",
"",
"",
""
],
"correct_index": 0,
"solution": "Count the cats in the picture one by one.
• Look carefully at the picture. • Count the cats: 1, 2, 3.
There are 3 cats.
Final Answer: 3\n"
},
{
"id": 6346,
"type": 2,
"question": "Count the number of stars: ",
"answers": [
"7",
"",
"",
""
],
"correct_index": 0,
"solution": "Count the stars in the picture one by one.
• Look carefully at the picture. • Count the stars: 1, 2, 3, 4, 5, 6, 7.
There are 7 stars.
Final Answer: 7\n"
},
{
"id": 6347,
"type": 2,
"question": "How many balloons are there? ",
"answers": [
"4",
"",
"",
""
],
"correct_index": 0,
"solution": "Count the balloons in the picture one by one.
• Look carefully at the picture. • Count the balloons: 1, 2, 3, 4.
There are 4 balloons.
Final Answer: 4\n"
},
{
"id": 6348,
"type": 2,
"question": "The number of books is .",
"answers": [
"6",
"",
"",
""
],
"correct_index": 0,
"solution": "Count the books in the picture one by one.
• Look carefully at the picture. • Count the books: 1, 2, 3, 4, 5, 6.
There are 6 books.
Final Answer: 6\n"
},
{
"id": 6390,
"type": 2,
"question": "There are ducks in the pond. If 2 ducks swim away, there will be 4 ducks left. How many ducks are swimming in the pond?",
"answers": [
"6",
"6",
"7",
"8"
],
"correct_index": null,
"solution": "\nWork backwards: after 2 ducks swim away, 4 ducks are left.
• Ducks at the start = ducks left + ducks that swam away • Ducks at the start = 4 + 2 • Ducks at the start = 6
There are 6 ducks swimming in the pond.
Final Answer: 6\n"
},
{
"id": 6399,
"type": 1,
"question": "If you have 4 pencils in one box and 2 pencils in another, how many pencils do you have in total?",
"answers": [
"5",
"6",
"4",
"None of the above"
],
"correct_index": 1,
"solution": "Add the number of pencils in both boxes.
• Pencils in first box = 4 • Pencils in second box = 2 • Total = 4 + 2 = 6
You have 6 pencils in total.
Final Answer: B: 6\n"
},
{
"id": 6400,
"type": 1,
"question": "If you have 5 apples in one basket and 3 apples in another, how many apples do you have in total?",
"answers": [
"7",
"8",
"5",
"None of the above"
],
"correct_index": 1,
"solution": "Add the apples in both baskets.
\r\n• 5 + 3 = 8 \r\n \r\nFinal Answer: 8"
},
{
"id": 6401,
"type": 1,
"question": "Sarah has 6 marbles in one jar and 4 marbles in another. How many marbles does Sarah have in total?",
"answers": [
"10",
"11",
"9",
"None of the above"
],
"correct_index": 0,
"solution": "Add the marbles in both jars.
\r\n• 6 + 4 = 10 \r\n \r\nFinal Answer: 10"
},
{
"id": 6408,
"type": 2,
"question": "Determine the total number of oranges in the box.",
"answers": [
"8",
"",
"",
""
],
"correct_index": 8,
"solution": "Count the oranges shown in the box.
\r\n• There are 8 oranges in total. \r\n \r\nFinal Answer: 8"
},
{
"id": 6409,
"type": 2,
"question": "Calculate the number of pencils on the table.",
"answers": [
"5",
"",
"",
""
],
"correct_index": 5,
"solution": "Count the pencils on the table.
\r\n• There are 5 pencils in total. \r\n \r\nFinal Answer: 5"
},
{
"id": 6410,
"type": 2,
"question": "Calculate the total number of apples in the basket.",
"answers": [
"8",
"",
"",
""
],
"correct_index": 8,
"solution": "Count the apples in the basket.
\r\n• There are 8 apples in total. \r\n \r\nFinal Answer: 8"
},
{
"id": 6411,
"type": 2,
"question": "Find out the total number of pencils on the desk.",
"answers": [
"5",
"",
"",
""
],
"correct_index": 5,
"solution": "Count the pencils on the desk.
\r\n• There are 5 pencils in total. \r\n \r\nFinal Answer: 5"
},
{
"id": 6414,
"type": 1,
"question": "Which 2-D shape represents a cylinder?",
"answers": [
"Circle",
"Triangle",
"Square",
"Rectangle"
],
"correct_index": 0,
"solution": "A cylinder has two circular faces at its ends. Its 2-D representation is a circle.
\r\n• The top and bottom of a cylinder are circles. \r\n \r\nFinal Answer: Circle"
},
{
"id": 6415,
"type": 1,
"question": "What does a square represent in the 2-D representation of a cube?",
"answers": [
"Base",
"Face",
"Edge",
"Vertex"
],
"correct_index": 1,
"solution": "A cube has 6 square faces. A square represents a face of the cube in 2-D.
\r\n• Each flat side of a cube is a face, and every face is a square. \r\n \r\nFinal Answer: Face"
},
{
"id": 6416,
"type": 1,
"question": "Which 2-D shape represents a cone?",
"answers": [
"Circle",
"Triangle",
"Square",
"Rectangle"
],
"correct_index": 1,
"solution": "When viewed from the side, a cone looks like a triangle. Its 2-D side-view representation is a triangle.
\r\n• The side view (profile) of a cone is triangular. \r\n \r\nFinal Answer: Triangle"
},
{
"id": 6417,
"type": 1,
"question": "Which 2-D shape represents a cylinder?",
"answers": [
"Circle",
"Triangle",
"Square",
"Rectangle"
],
"correct_index": 0,
"solution": "A cylinder has two circular faces. Its 2-D representation is a circle.
\r\n• The top and bottom faces of a cylinder are circles. \r\n \r\nFinal Answer: Circle"
},
{
"id": 6418,
"type": 1,
"question": "Which 2-D shape represents a pyramid?",
"answers": [
"Circle",
"Triangle",
"Square",
"Rectangle"
],
"correct_index": 1,
"solution": "When viewed from the side, a pyramid looks like a triangle. Its 2-D side-view representation is a triangle.
\r\n• The side faces of a pyramid are triangles, and the side view is a triangle. \r\n \r\nFinal Answer: Triangle"
},
{
"id": 6419,
"type": 1,
"question": "Which 2-D shape represents a cylinder?",
"answers": [
"Circle",
"Triangle",
"Square",
"Rectangle"
],
"correct_index": 0,
"solution": "A cylinder has two circular faces. Its 2-D representation is a circle.
\r\n• The top and bottom faces of a cylinder are circles. \r\n \r\nFinal Answer: Circle"
},
{
"id": 6420,
"type": 1,
"question": "What 2-D shape is associated with a cuboid?",
"answers": [
"Circle",
"Triangle",
"Square",
"Rectangle"
],
"correct_index": 3,
"solution": "A cuboid has 6 rectangular faces. Its 2-D representation is a rectangle.
\r\n• Each face of a cuboid is a rectangle (or square). \r\n \r\nFinal Answer: Rectangle"
},
{
"id": 6421,
"type": 1,
"question": "Which 2-D shape is associated with a cone?",
"answers": [
"Circle",
"Triangle",
"Square",
"Rectangle"
],
"correct_index": 0,
"solution": "A cone has a circular base. Its 2-D base representation is a circle.
\r\n• The bottom (base) of a cone is a circle. \r\n \r\nFinal Answer: Circle"
},
{
"id": 6423,
"type": 1,
"question": "Tom has 8 apples and 3 bananas. How many fruits does Tom have in total?",
"answers": [
"10",
"11",
"9",
"None of the above"
],
"correct_index": 1,
"solution": "Add the apples and bananas together.
\r\n• 8 + 3 = 11 \r\n \r\nFinal Answer: 11"
},
{
"id": 6424,
"type": 1,
"question": "Maria bought 5 red balloons and 7 blue balloons. How many balloons did Maria buy in total?",
"answers": [
"11",
"12",
"13",
"D) None of the above"
],
"correct_index": 1,
"solution": "Add the red and blue balloons.
\r\n• 5 + 7 = 12 \r\n \r\nFinal Answer: 12"
},
{
"id": 6425,
"type": 1,
"question": "Which number is the greatest?",
"answers": [
"21",
"20",
"22",
"23"
],
"correct_index": 3,
"solution": "Compare the numbers to find the greatest.
• List the numbers: 21, 20, 22, 23 • Compare tens: all have 2 tens (twenties). • Compare ones: 1, 0, 2, 3 — the largest ones digit is 3. • So 23 is the greatest.
Final Answer: D: 23\n"
},
{
"id": 6426,
"type": 1,
"question": "Which number is the smallest?",
"answers": [
"39",
"38",
"40",
"41"
],
"correct_index": 1,
"solution": "Compare the numbers to find the smallest.
• List the numbers: 39, 38, 40, 41 • Compare tens: 38 and 39 have 3 tens; 40 and 41 have 4 tens. • Numbers in the thirties are smaller than numbers in the forties. • Between 38 and 39, 38 is smaller because 8 < 9.
Final Answer: B: 38\n"
},
{
"id": 6427,
"type": 1,
"question": "Which number is the greatest?",
"answers": [
"36",
"37",
"35",
"34"
],
"correct_index": 1,
"solution": "Compare the numbers to find the greatest.
• List the numbers: 36, 37, 35, 34 • All numbers have 3 tens (thirties). • Compare ones: 6, 7, 5, 4 — the largest ones digit is 7. • So 37 is the greatest.
Final Answer: B: 37\n"
},
{
"id": 6428,
"type": 1,
"question": "Which number comes next in the sequence: 17, 20, 23, ...?",
"answers": [
"25",
"26",
"27",
"28"
],
"correct_index": 1,
"solution": "Find the pattern in the number sequence.
• From 17 to 20: add 3. • From 20 to 23: add 3. • The pattern is +3 each step. • Next number: 23 + 3 = 26.
Final Answer: B: 26\n"
},
{
"id": 6429,
"type": 2,
"question": "What is 16 + 9?",
"answers": [
"25",
"",
"",
""
],
"correct_index": 25,
"solution": "Add 16 and 9.
Final Answer: 32\r\n"
},
{
"id": 6480,
"type": 1,
"question": "How many letters are there in the word \"CROCODILE\" ?",
"answers": [
"8",
"9",
"10",
"7"
],
"correct_index": 1,
"solution": "Count each letter in the word CROCODILE.
\r\n• C-R-O-C-O-D-I-L-E = 9 letters \r\n \r\nFinal Answer: 9"
},
{
"id": 6493,
"type": 1,
"question": "How many letters are there in the word \"HIPPOPOTAMUS\" ?",
"answers": [
"11",
"10",
"12",
"9"
],
"correct_index": 2,
"solution": "Count each letter in the word "HIPPOPOTAMUS".
Final Answer: C: 12\n"
},
{
"id": 6519,
"type": 1,
"question": "How many letters are in the word 'TELEVISION'?",
"answers": [
"8",
"7",
"10",
"9"
],
"correct_index": 2,
"solution": "Count each letter in the word "TELEVISION".
Final Answer: C: 10\n"
},
{
"id": 6521,
"type": 1,
"question": "How many letters are in the word 'OCTOPUS'?",
"answers": [
"6",
"7",
"5",
"8"
],
"correct_index": 1,
"solution": "Count each letter in the word "OCTOPUS".
Final Answer: B: 7\n"
},
{
"id": 6523,
"type": 1,
"question": "How many letters are there in the word 'BUTTERFLY'?",
"answers": [
"10",
"9",
"8",
"11"
],
"correct_index": 1,
"solution": "Count each letter in the word "BUTTERFLY".
Final Answer: B: 9\n"
},
{
"id": 6524,
"type": 1,
"question": "How many letters are in the word 'CLASSROOM'?",
"answers": [
"8",
"7",
"6",
"9"
],
"correct_index": 3,
"solution": "Count each letter in the word "CLASSROOM".
Final Answer: D: 9\n"
},
{
"id": 6526,
"type": 1,
"question": "How many letters can you find in the word 'GORILLA'?",
"answers": [
"7",
"11",
"10",
"9"
],
"correct_index": 0,
"solution": "Count each letter in the word "GORILLA".
Final Answer: A: 7\n"
},
{
"id": 6527,
"type": 1,
"question": "How many letters can we count in the word 'WHALE'?",
"answers": [
"8",
"7",
"6",
"5"
],
"correct_index": 3,
"solution": "Count each letter in the word "WHALE".
• W-H-A-L-E • Count: 1-W, 2-H, 3-A, 4-L, 5-E
There are 5 letters in WHALE.
Final Answer: D: 5\n"
},
{
"id": 6528,
"type": 1,
"question": "How many letters are in the word 'MOTH'?",
"answers": [
"3",
"4",
"5",
"7"
],
"correct_index": 1,
"solution": "Count each letter in the word "MOTH".
• M-O-T-H • Count: 1-M, 2-O, 3-T, 4-H
There are 4 letters in MOTH.
Final Answer: B: 4\n"
},
{
"id": 6529,
"type": 1,
"question": "How many letters are in the word 'TOILET'?",
"answers": [
"8",
"7",
"6",
"9"
],
"correct_index": 2,
"solution": "Count each letter in the word "TOILET".
Final Answer: C: 6\n"
},
{
"id": 6530,
"type": 1,
"question": "How many letters are in the word 'CHEETAH'?",
"answers": [
"8",
"7",
"6",
"9"
],
"correct_index": 1,
"solution": "Count each letter in the word "CHEETAH".
Final Answer: B: 7\n"
},
{
"id": 6531,
"type": 1,
"question": "How many letters are in the word 'COCONUT'?",
"answers": [
"10",
"9",
"8",
"7"
],
"correct_index": 3,
"solution": "Count each letter in the word "COCONUT".
Final Answer: D: 7\n"
},
{
"id": 6532,
"type": 1,
"question": "How many letters are in the word 'SPARROW'?",
"answers": [
"9",
"11",
"8",
"7"
],
"correct_index": 3,
"solution": "Count each letter in the word "SPARROW".
Final Answer: D: 7\n"
},
{
"id": 6535,
"type": 1,
"question": "How do you write the number 19 in words?",
"answers": [
"sixteen",
"nineteen",
"twenty",
"None of the above"
],
"correct_index": 1,
"solution": "Recall how to write the number 19 in words.
• 19 is made of 10 + 9. • 10 in words is "ten" and 9 in words is "nine". • But 19 is NOT "ten nine" — it is "nineteen".
19 is written as "nineteen" in words.
Final Answer: B: nineteen\n"
},
{
"id": 6540,
"type": 1,
"question": "How do you write the number 13 in words?",
"answers": [
"thirteen",
"thirteenth",
"twelfth",
"tirteen"
],
"correct_index": 0,
"solution": "The number 13 in words is 'thirteen' — formed from 'thir' with the '-teen' suffix.
\r\nFinal Answer: thirteen"
},
{
"id": 6560,
"type": 1,
"question": "Which word has more letters? CAT OR MOUSE?",
"answers": [
"CAT",
"MOUSE",
"Don't know",
"Same"
],
"correct_index": 1,
"solution": "Count the letters in each word.
\r\nMOUSE has more letters. \r\nFinal Answer: MOUSE"
},
{
"id": 6566,
"type": 1,
"question": "Which word has less letters? RAIN or STORM?",
"answers": [
"STORM",
"RAIN",
"Don't know",
"Both have the same"
],
"correct_index": 1,
"solution": "Count the letters in each word.
\r\nRAIN has fewer letters. \r\nFinal Answer: RAIN"
},
{
"id": 6570,
"type": 1,
"question": "MOTHER, FATHER, DAUGHTER. Which 2 words have the same number of letters?",
"answers": [
"MOTHER and DAUGHTER",
"MOTHER and FATHER",
"FATHER and DAUGHTER",
"I do not know"
],
"correct_index": 1,
"solution": "Count the letters in each word.
\r\nMOTHER and FATHER both have 6 letters each. \r\nFinal Answer: MOTHER and FATHER"
},
{
"id": 6572,
"type": 1,
"question": "APPLE, BANANA, GRAPE. Which 2 words have the same number of letters?",
"answers": [
"APPLE and BANANA",
"APPLE and GRAPE",
"BANANA and GRAPE",
"NO ANSWER"
],
"correct_index": 1,
"solution": "Count the letters in each word.
\r\nAPPLE and GRAPE both have 5 letters each. \r\nFinal Answer: APPLE and GRAPE"
},
{
"id": 6573,
"type": 1,
"question": "SUN, MOON, STAR. Which 2 words have the same number of letters?",
"answers": [
"SUN and STAR",
"SUN and MOON",
"MOON and STAR",
"NO ANSWER"
],
"correct_index": 2,
"solution": "Count the letters in each word:
\r\n• SUN = 3 letters \r\n• MOON = 4 letters \r\n• STAR = 4 letters
\r\nMOON and STAR both have 4 letters, so they have the same number of letters. \r\n \r\nFinal Answer: MOON and STAR"
},
{
"id": 6586,
"type": 1,
"question": "What are the 2 numbers that come next in the sequence: 6, 8, 10, ___, ___?",
"answers": [
"11, 12",
"12, 13",
"12, 14",
"11, 13"
],
"correct_index": 2,
"solution": "The sequence increases by 2 each time.
\r\nThe next two numbers are 12 and 14. \r\nFinal Answer: 12, 14"
},
{
"id": 6628,
"type": 1,
"question": "When 5 litres of water is poured into an empty rectangular tank of height 20 cm, 800 cm3 of water overflows. What is the base area of the tank?",
"answers": [
"120 $cm^2$",
"210 $cm^2$",
"150 $cm^2$",
"200 $cm^2$"
],
"correct_index": 1,
"solution": "Convert litres to cubic centimetres, then find how much water stays in the tank.
\r\n• 5 litres = 5000 cm³ \r\n• Overflow = 800 cm³ \r\n• Water that stays = 5000 − 800 = 4200 cm³ \r\n• Water fills the tank to its full height of 20 cm \r\n• Base area × 20 = 4200 \r\n• Base area = 4200 ÷ 20 = 210 cm²
\r\nFinal Answer: 210 cm²"
},
{
"id": 6634,
"type": 1,
"question": "A rectangular tank measuring 80 cm by 50 cm was 75% filled with water. When 64 litres of water were poured out, it was only $$\\dfrac{1}{4}$$ full. Find the height of the tank.",
"answers": [
"30 cm",
"34 cm",
"32 cm",
"42 cm"
],
"correct_index": 2,
"solution": "Base area of the tank = 80 × 50 = 4000 cm².
\r\n• Initially 75% full, then water poured out until 25% full. \r\n• Fraction of water poured out = 75% − 25% = 50% of the tank. \r\n• 50% of tank = 64 litres = 64000 cm³. \r\n• 100% of tank = 64000 × 2 = 128000 cm³. \r\n• Height = Volume ÷ Base area = 128000 ÷ 4000 = 32 cm. \r\n \r\nFinal Answer: 32 cm"
},
{
"id": 6635,
"type": 1,
"question": "A rectangular tank, 40 cm long, 25 cm wide and 12 cm tall, was filled with 6 litres of water. Some of the water was poured out from the rectangular tank to fill a cubic tank of height 10 cm to its brim. What was the height of the remaining amount of water in the rectangular tank?",
"answers": [
"1 cm",
"10 cm",
"5 cm",
"8 cm"
],
"correct_index": 2,
"solution": "Base area of rectangular tank = 40 × 25 = 1000 cm².
\r\n• Initial water volume = 6 litres = 6000 cm³. \r\n• Initial water height = 6000 ÷ 1000 = 6 cm. \r\n• Water poured into cubic tank = 10 × 10 × 10 = 1000 cm³. \r\n• Remaining water = 6000 − 1000 = 5000 cm³. \r\n• Remaining height = 5000 ÷ 1000 = 5 cm. \r\n \r\nFinal Answer: 5 cm"
},
{
"id": 6636,
"type": 1,
"question": "A box measures 100 cm by 40 cm and is filled with sand to 60% of its height. After removing 30 liters of sand, it is now $$\\dfrac{1}{5}$$ full. What is the height of the box?",
"answers": [
"20.5 cm",
"30 cm",
"18.75 cm",
"40 cm"
],
"correct_index": 2,
"solution": "Let the height of the box be \\(h\\) cm. Use the change in sand volume.
\r\n• Base area = 100 × 40 = 4000 cm² \r\n• Initial sand = 60% full = 0.6 × 4000 × h = 2400h cm³ \r\n• After removing 30 L (30000 cm³): sand = \\(\\frac{1}{5}\\) full = 0.2 × 4000 × h = 800h cm³ \r\n• 2400h − 30000 = 800h \r\n• 1600h = 30000 \r\n• \\(h = \\frac{30000}{1600} = 18.75\\) cm
\r\nFinal Answer: 18.75 cm"
},
{
"id": 6641,
"type": 1,
"question": "A rectangular tank was filled with oil to a height of 8 cm. Its rectangular base measured 30 cm by 25 cm. When 9 litres of oil were poured into the tank, the oil level rose to $$\\dfrac{4}{5}$$ of the height of the tank. Find the height of the tank.",
"answers": [
"15 cm",
"20 cm",
"30 cm",
"25 cm"
],
"correct_index": 3,
"solution": "Find the total oil volume after adding 9 litres, then relate to the tank height.
\r\n• Base area = 30 × 25 = 750 cm² \r\n• Initial oil = 750 × 8 = 6000 cm³ \r\n• 9 litres added = 9000 cm³ \r\n• Total oil = 6000 + 9000 = 15000 cm³ \r\n• \\(\\frac{4}{5}\\) of tank height corresponds to 15000 cm³ \r\n• Oil height = 15000 ÷ 750 = 20 cm \r\n• \\(\\frac{4}{5}\\) × tank height = 20 cm \r\n• Tank height = 20 × \\(\\frac{5}{4}\\) = 25 cm
\r\nFinal Answer: 25 cm"
},
{
"id": 6647,
"type": 1,
"question": "A rectangular tank, 36 cm long, 25 cm wide and 24 cm high was $$\\dfrac{3}{8}$$ filled with some water. Sam added fifteen 750 ml bottles full of water into the tank. What was the water level from the brim of the tank?",
"answers": [
"5.5 cm",
"5 cm",
"3.5 cm",
"2.5 cm"
],
"correct_index": 3,
"solution": "Find the total water volume, compute the water height, then find the gap from the brim.
\r\n• Tank volume = 36 × 25 × 24 = 21600 cm³ \r\n• Initial water = \\(\\frac{3}{8}\\) × 21600 = 8100 cm³ \r\n• Water added = 15 × 750 ml = 11250 cm³ \r\n• Total water = 8100 + 11250 = 19350 cm³ \r\n• Base area = 36 × 25 = 900 cm² \r\n• Water height = 19350 ÷ 900 = 21.5 cm \r\n• Distance from brim = 24 − 21.5 = 2.5 cm
\r\nFinal Answer: 2.5 cm"
},
{
"id": 6649,
"type": 1,
"question": "A rectangular tank, 30 cm long and 24 cm wide, contains water to a depth of 6 cm. When the water is transferred to a tank of height 12 com, it becomes $$\\dfrac{1}{4}$$ full. Find the base area of the new tank.",
"answers": [
"1240 $cm^2$",
"1540 $cm^2$",
"1440 $cm^2$",
"1220 $cm^2$"
],
"correct_index": 2,
"solution": "The volume of water stays the same when transferred.
\r\n• Water volume = 30 × 24 × 6 = 4320 cm³ \r\n• In the new tank: \\(\\frac{1}{4}\\) full at height 12 cm \r\n• \\(\\frac{1}{4}\\) × base area × 12 = 4320 \r\n• 3 × base area = 4320 \r\n• Base area = 4320 ÷ 3 = 1440 cm²
\r\nFinal Answer: 1440 cm²"
},
{
"id": 6657,
"type": 1,
"question": "An empty rectangular tank measures 40 cm long, 36 cm wide and 30 cm high. 25.272 litres of water were poured into the tank. What was the height of the water in the tank?",
"answers": [
"16.55 cm",
"20 cm",
"18.65 cm",
"17.55 cm"
],
"correct_index": 3,
"solution": "Convert litres to cubic centimetres, then divide by the base area.
\r\n• Water volume = 25.272 L = 25272 cm³ \r\n• Base area = 40 × 36 = 1440 cm² \r\n• Water height = 25272 ÷ 1440 = 17.55 cm
\r\nFinal Answer: 17.55 cm"
},
{
"id": 6674,
"type": 1,
"question": "A cube with side 15 cm is melted down and recast into smaller cubes, each with side 5 cm. How many smaller cubes can be formed?",
"answers": [
"12",
"27",
"24",
"45"
],
"correct_index": 1,
"solution": "Find the volume of the big cube, then divide by the volume of one small cube.
\r\n• Big cube volume = 15³ = 15 × 15 × 15 = 3375 cm³ \r\n• Small cube volume = 5³ = 5 × 5 × 5 = 125 cm³ \r\n• Number of small cubes = 3375 ÷ 125 = 27
\r\nFinal Answer: 27"
},
{
"id": 6675,
"type": 1,
"question": "A large cube has a volume of 512 cm³. It is melted and recast into 8 identical smaller cubes. Find the side length of each smaller cube.",
"answers": [
"2",
"8",
"4",
"16"
],
"correct_index": 2,
"solution": "Divide the total volume by 8, then take the cube root.
\r\n• Volume of each small cube = 512 ÷ 8 = 64 cm³ \r\n• Side = \\(\\sqrt[3]{64} = 4\\) cm (since 4³ = 64)
\r\nFinal Answer: 4 cm"
},
{
"id": 6676,
"type": 1,
"question": "A cube-shaped tank of side 18 cm is filled with water. The water is then poured into another cube-shaped tank of side 9 cm. How many of the smaller tanks can be filled?",
"answers": [
"4",
"16",
"8",
"32"
],
"correct_index": 2,
"solution": "Find the volume of the big tank, then divide by the volume of one small tank.
\r\n• Big cube volume = 18³ = 18 × 18 × 18 = 5832 cm³ \r\n• Small cube volume = 9³ = 9 × 9 × 9 = 729 cm³ \r\n• Number of small tanks = 5832 ÷ 729 = 8
\r\nFinal Answer: 8"
},
{
"id": 6677,
"type": 1,
"question": "A cuboid tank (24 x 15 x 10) cm is full. The water is poured into a cuboid with base (20 x 12) cm to a height (h). Find (h).",
"answers": [
"10 cm",
"20 cm",
"22 cm",
"15 cm"
],
"correct_index": 3,
"solution": "Volume of water in first tank = 24 × 15 × 10 = 3600 cm³.
\r\n• Base area of second tank = 20 × 12 = 240 cm². \r\n• Height h = Volume ÷ Base area \r\n• h = 3600 ÷ 240 = 15 cm. \r\n \r\nFinal Answer: 15 cm"
},
{
"id": 6678,
"type": 1,
"question": "A cube of side 18 cm is recast into cubes of side 3 cm. How many small cubes are formed?",
"answers": [
"56",
"216",
"96",
"188"
],
"correct_index": 1,
"solution": "Find the volume of the big cube, then divide by the volume of one small cube.
\r\n• Big cube volume = 18³ = 18 × 18 × 18 = 5832 cm³ \r\n• Small cube volume = 3³ = 3 × 3 × 3 = 27 cm³ \r\n• Number of small cubes = 5832 ÷ 27 = 216
\r\nFinal Answer: 216"
},
{
"id": 6680,
"type": 1,
"question": "A cuboid (40 x 20 x 10) cm is poured equally into 8 identical cubes. Find the side of each cube.",
"answers": [
"10 cm",
"20 cm",
"6 cm",
"8 cm"
],
"correct_index": 0,
"solution": "Find the total volume, divide by 8, then take the cube root.
\r\nFinal Answer: 10 cm"
},
{
"id": 6681,
"type": 1,
"question": "A cuboid (25 x 14 x 10) cm of water is poured into another cuboid with base (35 x 10) cm. Find the water height.",
"answers": [
"12 cm",
"14 cm",
"10 cm",
"20 cm"
],
"correct_index": 2,
"solution": "Find the water volume, then divide by the new base area.
\r\n• Water volume = 25 × 14 × 10 = 3500 cm³ \r\n• New base area = 35 × 10 = 350 cm² \r\n• Water height = 3500 ÷ 350 = 10 cm
\r\nFinal Answer: 10 cm"
},
{
"id": 6682,
"type": 1,
"question": "How many cubes of side 4 cm fit exactly in a cuboid (24 x 16 x 8) cm?",
"answers": [
"24",
"48",
"58",
"12"
],
"correct_index": 1,
"solution": "Find how many cubes fit along each dimension, then multiply.
\r\n• Along 24 cm: 24 ÷ 4 = 6 cubes \r\n• Along 16 cm: 16 ÷ 4 = 4 cubes \r\n• Along 8 cm: 8 ÷ 4 = 2 cubes \r\n• Total = 6 × 4 × 2 = 48
\r\nFinal Answer: 48"
},
{
"id": 6683,
"type": 1,
"question": "A cuboid (27 x 9 x 3) cm is recast into a single cube. Find the cube’s side.",
"answers": [
"9 cm",
"13 cm",
"14 cm",
"11 cm"
],
"correct_index": 0,
"solution": "Find the volume of the cuboid, then take the cube root.
\r\nFinal Answer: 9 cm"
},
{
"id": 6684,
"type": 1,
"question": "A cube of side 20 cm is filled only to a height of 12 cm. The water is poured into a cuboid with base (16 x 10) cm. Find the new height.",
"answers": [
"20 cm",
"22 cm",
"28 cm",
"30 cm"
],
"correct_index": 3,
"solution": "Find the water volume in the cube, then divide by the cuboid base area.
\r\n• Water volume = 20 × 20 × 12 = 4800 cm³ \r\n• New base area = 16 × 10 = 160 cm² \r\n• New height = 4800 ÷ 160 = 30 cm
\r\nFinal Answer: 30 cm"
},
{
"id": 6685,
"type": 1,
"question": "Water from a completely filled cuboid (40 x 25 x 9) cm is poured equally into 50 identical small cuboids, each with base (10 x 6) cm. Find the height of water in each small cuboid.",
"answers": [
"3 cm",
"4 cm",
"6 cm",
"2 cm"
],
"correct_index": 0,
"solution": "Find total volume, divide by 50, then divide by the small base area.
\r\n• Total water = 40 × 25 × 9 = 9000 cm³ \r\n• Each small cuboid gets = 9000 ÷ 50 = 180 cm³ \r\n• Base area of each small = 10 × 6 = 60 cm² \r\n• Height in each = 180 ÷ 60 = 3 cm
\r\nFinal Answer: 11"
},
{
"id": 6726,
"type": 1,
"question": "A tank with base (12 × 9) c𝑚 receives all the water from a cube of side 12 𝑐𝑚, then all the water from a cube of side \r\n6 cm. The tank was empty at first. Find the final water height.",
"answers": [
"16 cm",
"18 cm",
"20 cm",
"22 cm"
],
"correct_index": 1,
"solution": "Find the total water volume from both cubes, then divide by the tank base area.
\r\n• Cube 1 (side 12 cm): volume = 12³ = 1728 cm³ \r\n• Cube 2 (side 6 cm): volume = 6³ = 216 cm³ \r\n• Total water = 1728 + 216 = 1944 cm³ \r\n• Tank base area = 12 × 9 = 108 cm² \r\n• Water height = 1944 ÷ 108 = 18 cm
\r\nFinal Answer: 18 cm"
},
{
"id": 6727,
"type": 1,
"question": "A cuboid has length 21cm, height 8cm, and volume 2016 $cm^3$. Find its width.",
"answers": [
"12 cm",
"10 cm",
"11 cm",
"13 cm"
],
"correct_index": 0,
"solution": "Use the volume formula: Volume = Length × Width × Height.
\r\nFinal Answer: 12 cm"
},
{
"id": 6728,
"type": 1,
"question": "Water from a completely filled cuboid 30 x 14 x 12 cm is poured equally into 9 identical cuboids. Each small cuboid has base (10 × 8) cm. Find the common height.",
"answers": [
"6 cm",
"7 cm",
"8 cm",
"9 cm"
],
"correct_index": 1,
"solution": "Find total volume, divide by 9, then divide by the small base area.
\r\n• Total water = 30 × 14 × 12 = 5040 cm³ \r\n• Each small cuboid = 5040 ÷ 9 = 560 cm³ \r\n• Base of each = 10 × 8 = 80 cm² \r\n• Height = 560 ÷ 80 = 7 cm
\r\nFinal Answer: 7 cm"
},
{
"id": 6729,
"type": 1,
"question": "A cuboid has length 12cm, width 8cm, height 36cm. Its volume is kept the same, but the length is doubled and the width is tripled. Find the new height.",
"answers": [
"6 cm",
"7 cm",
"5 cm",
"8 cm"
],
"correct_index": 0,
"solution": "The volume stays the same. Find the original volume, then divide by the new base area.
\r\n• Original volume = 12 × 8 × 36 = 3456 cm³ \r\n• New length = 12 × 2 = 24 cm \r\n• New width = 8 × 3 = 24 cm \r\n• New base area = 24 × 24 = 576 cm² \r\n• New height = 3456 ÷ 576 = 6 cm
\r\nFinal Answer: 6 cm"
},
{
"id": 6730,
"type": 1,
"question": "How many cubes of side 8cm are needed to fill a tank with base (32×16) cm to a height of 8 cm?",
"answers": [
"10",
"9",
"7",
"8"
],
"correct_index": 3,
"solution": "Find the volume to fill and divide by the volume of one cube.
\r\n• Volume to fill = 32 × 16 × 8 = 4096 cm³ \r\n• Each cube volume = 8³ = 512 cm³ \r\n• Number of cubes = 4096 ÷ 512 = 8
\r\nFinal Answer: 8"
},
{
"id": 6731,
"type": 1,
"question": "A solid cuboid measures 30×20×12cm. A rectangular void of 10×5×12cm is removed from the interior. Find the remaining volume.",
"answers": [
"7200 $cm^3$",
"7000 $cm^3$",
"6600 $cm^3$",
"6800 $cm^3$"
],
"correct_index": 2,
"solution": "Find the total volume, subtract the volume of the void.
\r\nFinal Answer: 6600 cm³"
},
{
"id": 6732,
"type": 1,
"question": "A tank 24×10×9cm and a tank 18×12×5cm are both full. All water is poured into a single empty tank with base \r\n((12×9) cm. Find the final height.",
"answers": [
"30 cm",
"28 cm",
"40 cm",
"32 cm"
],
"correct_index": 0,
"solution": "Find the total water volume from both tanks, then divide by the new tank's base area.
\r\n• Tank 1: 24 × 10 × 9 = 2160 cm³ \r\n• Tank 2: 18 × 12 × 5 = 1080 cm³ \r\n• Total water = 2160 + 1080 = 3240 cm³ \r\n• New tank base area = 12 × 9 = 108 cm² \r\n• Height = 3240 ÷ 108 = 30 cm
\r\nFinal Answer: 30 cm"
},
{
"id": 6733,
"type": 1,
"question": "All the water from a cuboid with base area 196 $cm^2$ and height 14 is poured into a cube, filling it to the brim. Find the cube’s side.",
"answers": [
"12 cm",
"10 cm",
"11 cm",
"14 cm"
],
"correct_index": 3,
"solution": "Find the volume of water, then take the cube root since a cube has equal sides.
\r\n• Water volume = 196 × 14 = 2744 cm³ \r\n• Cube side = \\(\\sqrt[3]{2744} = 14\\) cm (since 14³ = 2744)
\r\nFinal Answer: 14 cm"
},
{
"id": 6734,
"type": 1,
"question": "A cuboid has L=20cm, W=15cm, H=12cm. The height is increased by 25% and the length is decreased by 20%, width unchanged. Find the new volume.",
"answers": [
"1800 $cm^3$",
"3200 $cm^3$",
"3600 $cm^3$",
"3800 $cm^3$"
],
"correct_index": 2,
"solution": "Original volume = 20 × 15 × 12 = 3600 cm³.
New height = 12 × 1.25 = 15 cm. New length = 20 × 0.80 = 16 cm. Width unchanged = 15 cm.
• New volume = 16 × 15 × 15 = 3600 cm³.
Final Answer: 3600 cm³"
},
{
"id": 6735,
"type": 1,
"question": "A cuboid 24×10×9 cm and a cuboid 18×12×5 cm are each filled to the brim. All their water is poured into a single empty tank that will be filled to a height of 12cm. The target tank has length 30 cm and unknown width w cm. Find \r\n𝑤.",
"answers": [
"8 cm",
"9 cm",
"10 cm",
"11 cm"
],
"correct_index": 1,
"solution": "The volume of water from both cuboids equals the volume in the tank.
• Volume of first cuboid = 24 × 10 × 9 = 2160 cm³ • Volume of second cuboid = 18 × 12 × 5 = 1080 cm³ • Total water = 2160 + 1080 = 3240 cm³
Tank volume = base area × height = 30 × w × 12 = 360w. 360w = 3240 w = 3240 ÷ 360 = 9 cm.
Final Answer: 9 cm"
},
{
"id": 6736,
"type": 1,
"question": "A cuboid with dimensions 24×w×15 cm is filled to the brim. All the water is poured into a cube of side 30 cm, filling it to the brim. Find w.",
"answers": [
"30 cm",
"60 cm",
"75 cm",
"80 cm"
],
"correct_index": 2,
"solution": "The volume of the cuboid equals the volume of the cube.
Volume of cube = 30³ = 27000 cm³. Volume of cuboid = 24 × w × 15 = 360w.
360w = 27000 w = 27000 ÷ 360 = 75 cm.
Final Answer: 75 cm"
},
{
"id": 6737,
"type": 1,
"question": "A cube of side s cm is filled to the brim. All the water is poured equally into five identical cuboids, each with base 20 × 8cm, reaching a common height of 10 cm. Find 𝑠.",
"answers": [
"16 cm",
"22 cm",
"18 cm",
"20 cm"
],
"correct_index": 3,
"solution": "The cube's water is equally split among 5 cuboids. Total volume is conserved.
Volume of one cuboid = 20 × 8 × 10 = 1600 cm³. Total volume of 5 cuboids = 5 × 1600 = 8000 cm³. So the cube's volume = 8000 cm³.
s³ = 8000 s = \\( \\sqrt[3]{8000} \\) = 20 cm.
Final Answer: 20 cm"
},
{
"id": 6738,
"type": 1,
"question": "A cuboid has dimensions 12×8×36 cm. A new cuboid has the same volume, but its length is doubled and its width is tripled. Find the new height.",
"answers": [
"6 cm",
"4 cm",
"8 cm",
"10 cm"
],
"correct_index": 0,
"solution": "Original volume = 12 × 8 × 36 = 3456 cm³.
New length = 12 × 2 = 24 cm. New width = 8 × 3 = 24 cm. New volume (same) = 24 × 24 × h = 3456.
h = 3456 ÷ (24 × 24) = 3456 ÷ 576 = 6 cm.
Final Answer: 6 cm"
},
{
"id": 6739,
"type": 1,
"question": "A cuboid 24×15×6 cm and a cuboid 18×12×5 cm are both filled to the brim. All their water is poured into a single empty tank with base 24×w cm and the water rises to a height of 9 cm. Find w.",
"answers": [
"12 cm",
"10 cm",
"15 cm",
"25 cm"
],
"correct_index": 2,
"solution": "Total water volume = sum of volumes of both cuboids.
• First cuboid: 24 × 15 × 6 = 2160 cm³ • Second cuboid: 18 × 12 × 5 = 1080 cm³ • Total water = 2160 + 1080 = 3240 cm³
Tank volume = 24 × w × 9 = 216w. 216w = 3240 w = 3240 ÷ 216 = 15 cm.
Final Answer: 15 cm"
},
{
"id": 6740,
"type": 1,
"question": "A cube of side 18 cm is filled to the brim. All the water is poured equally into three cuboids, each filling to a common height of 9 cm. Two bases are 12×18 cm and 24×9 cm. The third base is 27×w cm. Find w.",
"answers": [
"10 cm",
"8 cm",
"12 cm",
"6 cm"
],
"correct_index": 1,
"solution": "Volume of cube = 18³ = 5832 cm³. Split equally among 3 cuboids: each gets 5832 ÷ 3 = 1944 cm³.
Each cuboid has height 9 cm, so base area = 1944 ÷ 9 = 216 cm².
Check the known bases: • 12 × 18 = 216 ✓ • 24 × 9 = 216 ✓ • 27 × w = 216 → w = 216 ÷ 27 = 8 cm.
Final Answer: 8 cm"
},
{
"id": 6741,
"type": 1,
"question": "A cuboid with dimensions 28×w×14 cm is filled to the brim. All the water is poured into a cube of side 28 cm, filling the cube to the brim. Find w.",
"answers": [
"36 cm",
"54 cm",
"52 cm",
"56 cm"
],
"correct_index": 3,
"solution": "The volume of the cuboid equals the volume of the cube.
Volume of cube = 28³ = 21952 cm³. Volume of cuboid = 28 × w × 14 = 392w.
392w = 21952 w = 21952 ÷ 392 = 56 cm.
Final Answer: 56 cm"
},
{
"id": 6742,
"type": 1,
"question": "A cube of side s cm is poured equally into 4 identical cuboids. Then the water from two of these cuboids is combined into a tank with base 24×9 cm, producing a height of 4 cm. Find s.",
"answers": [
"8 cm",
"10 cm",
"12 cm",
"22 cm"
],
"correct_index": 2,
"solution": "Let the cube's volume be s³. Split equally into 4 cuboids, each gets s³/4.
Water from two of them = 2 × (s³/4) = s³/2. This fills a tank with base 24 × 9 cm to height 4 cm: Volume in tank = 24 × 9 × 4 = 864 cm³.
s³/2 = 864 s³ = 1728 s = \\( \\sqrt[3]{1728} \\) = 12 cm.
Final Answer: 12 cm"
},
{
"id": 6743,
"type": 1,
"question": "A cube of side s cm is poured equally into 6 identical cuboids, each with base 15×12 cm. Then the water from four of these cuboids is poured into a single tank with base 24×6 cm, producing a height of 8 cm. Find s.",
"answers": [
"12 cm",
"11 cm",
"10 cm",
"8 cm"
],
"correct_index": 0,
"solution": "Let the cube's volume be s³. Split equally into 6 cuboids, each gets s³/6.
Water from four of them = 4 × (s³/6) = 2s³/3. This fills a tank with base 24 × 6 cm to height 8 cm: Volume in tank = 24 × 6 × 8 = 1152 cm³.
2s³/3 = 1152 s³ = 1152 × (3/2) = 1728 s = \\( \\sqrt[3]{1728} \\) = 12 cm.
Final Answer: 12 cm"
},
{
"id": 6744,
"type": 1,
"question": "A car travels 180 km in 3 h. Find its speed.",
"answers": [
"540 kmh",
"60 km/h",
"60 kmh",
"50 km/h"
],
"correct_index": 1,
"solution": "Speed = Distance ÷ Time.
• Distance = 180 km • Time = 3 h • Speed = 180 ÷ 3 = 60 km/h
Final Answer: 60 km/h"
},
{
"id": 6756,
"type": 1,
"question": "A 200 m train crosses a 300 m bridge at 20 m/s. Time to get completely over?",
"answers": [
"20 s",
"100 s",
"25 s",
"250 s"
],
"correct_index": 2,
"solution": "To completely cross the bridge, the train must travel its own length plus the bridge length.
• Total distance = train length + bridge length = 200 + 300 = 500 m. • Speed = 20 m/s. • Time = 500 ÷ 20 = 25 s.
Final Answer: 25 s"
},
{
"id": 6759,
"type": 1,
"question": "Two cyclists ride same direction at 18 km/h and 24 km/h. When will they be 30 km apart?",
"answers": [
"1 h",
"4 h",
"5 h",
"10 h"
],
"correct_index": 2,
"solution": "Same direction → relative speed = difference of speeds.
• Relative speed = 24 − 18 = 6 km/h. • Time to be 30 km apart = 30 ÷ 6 = 5 h.
Final Answer: 5 h"
},
{
"id": 6760,
"type": 1,
"question": "Still-air speed of plane = 500 km/h. Tailwind/headwind = 50 km/h. The plane took 2 h to make a return trip (point A to B and back to A). What is the distance between A and B?",
"answers": [
"500 km",
"495 km",
"400 km",
"395 km"
],
"correct_index": 1,
"solution": "Let the one-way distance be D km.
• With tailwind (A to B): speed = 500 + 50 = 550 km/h, time = D/550. • With headwind (B to A): speed = 500 − 50 = 450 km/h, time = D/450. • Total time = 2 h.
D/550 + D/450 = 2 D × (1/550 + 1/450) = 2 D × ((450 + 550)/(550 × 450)) = 2 D × (1000/247500) = 2 D = 2 × 247500/1000 = 2 × 247.5 = 495 km.
Final Answer: 495 km"
},
{
"id": 6764,
"type": 1,
"question": "A boat’s still-water speed is 12 km/h. The current is 2 km/h. It travels from a pier to a town downstream and returns to the pier. The total time is 6 h. Find the one-way distance D from the pier to the town.",
"answers": [
"25 km",
"35 km",
"30 km",
"40 km"
],
"correct_index": 1,
"solution": "Let the one-way distance be D km.
• Downstream speed = 12 + 2 = 14 km/h, time = D/14. • Upstream speed = 12 − 2 = 10 km/h, time = D/10. • Total time = 6 h.
D/14 + D/10 = 6 D × (1/14 + 1/10) = 6 D × ((10 + 14)/140) = 6 D × (24/140) = 6 D = 6 × 140/24 = 6 × (35/6) = 35 km.
Final Answer: 35 km"
},
{
"id": 6765,
"type": 1,
"question": "A train passes a pole in 12 s and a 180 m platform in 24 s, both at constant speed. Find the train’s length.",
"answers": [
"120 m",
"150 m",
"180 m",
"200 m"
],
"correct_index": 2,
"solution": "Let the train's length be L m and speed be v m/s.
• Passing a pole: distance = L, time = 12 s → v = L/12. • Passing a 180 m platform: distance = L + 180, time = 24 s → v = (L + 180)/24.
L/12 = (L + 180)/24 2L = L + 180 L = 180 m.
Final Answer: 180 m"
},
{
"id": 6767,
"type": 1,
"question": "A cyclist rides at 15 km/h for 4 hours. How far does the cyclist travel?",
"answers": [
"40 km",
"50 km",
"60 km",
"80 km"
],
"correct_index": 2,
"solution": "Distance = Speed × Time.
• Distance = 15 km/h × 4 h = 60 km.
Final Answer: 60 km"
},
{
"id": 6771,
"type": 1,
"question": "A runner maintains 4 m/s for 12 min. How many meters does the runner cover?",
"answers": [
"3000 m",
"2640 m",
"2880 m",
"3200 m"
],
"correct_index": 2,
"solution": "Convert minutes to seconds, then find distance.
• 12 min = 12 × 60 = 720 s. • Distance = 4 m/s × 720 s = 2880 m.
Final Answer: 2880 m"
},
{
"id": 6778,
"type": 1,
"question": "A jogger plans to complete 10 km at a steady 8 km/h. How many minutes will the run take?",
"answers": [
"60 min",
"70 min",
"75 min",
"90 min"
],
"correct_index": 2,
"solution": "Time = Distance ÷ Speed.
• Time in hours = 10 ÷ 8 = 1.25 h. • Convert to minutes: 1.25 × 60 = 75 min.
Final Answer: 75 min"
},
{
"id": 6786,
"type": 1,
"question": "A cyclist rides three equal 30-km segments at 30 km/h, 45 km/h, and 90 km/h. What is the trip’s average speed?",
"answers": [
"30 km/h",
"40 km/h",
"45 km/h",
"50 km/h"
],
"correct_index": 2,
"solution": "Average speed = Total distance ÷ Total time.
\n• Total distance = 3 × 30 = 90 km. \n• Time for each segment: \n• Segment 1: 30 ÷ 30 = 1 h \n• Segment 2: 30 ÷ 45 = \\(\\frac{2}{3}\\) h \n• Segment 3: 30 ÷ 90 = \\(\\frac{1}{3}\\) h \n• Total time = 1 + \\(\\frac{2}{3}\\) + \\(\\frac{1}{3}\\) = 2 h. \n• Average speed = 90 ÷ 2 = 45 km/h. \n \nFinal Answer: 45 km/h"
},
{
"id": 6787,
"type": 1,
"question": "A 320-km journey must have overall average 80 km/h. The first 80 km are at 40 km/h and the next 80 km at 80 km/h. What constant speed is needed for the remaining distance to meet the target average?",
"answers": [
"120 km/h",
"140 km/h",
"150 km/h",
"160 km/h"
],
"correct_index": 3,
"solution": "Target total time = Total distance ÷ Target average speed.
\r\n• Target time = 320 ÷ 80 = 4 h. \r\n• Time used so far: \r\n• First 80 km at 40 km/h: 80 ÷ 40 = 2 h. \r\n• Next 80 km at 80 km/h: 80 ÷ 80 = 1 h. \r\n• Total time used = 2 + 1 = 3 h. \r\n• Remaining time = 4 − 3 = 1 h. \r\n• Remaining distance = 320 − 80 − 80 = 160 km. \r\n• Required speed = 160 ÷ 1 = 160 km/h. \r\n \r\nFinal Answer: 160 km/h"
},
{
"id": 6788,
"type": 1,
"question": "A 60-km loop has three 20-km segments at 60, 120, and 30 km/h. At the end of each segment, the bus dwells 10 minutes. What is the average speed for the loop including all dwell times?",
"answers": [
"26 km/h",
"32 km/h",
"34 km/h",
"36 km/h"
],
"correct_index": 3,
"solution": "Average speed = Total distance ÷ Total time (including dwells).
\n• Total distance = 60 km. \n• Driving times: \n• Segment 1: 20 ÷ 60 = \\(\\frac{1}{3}\\) h \n• Segment 2: 20 ÷ 120 = \\(\\frac{1}{6}\\) h \n• Segment 3: 20 ÷ 30 = \\(\\frac{2}{3}\\) h \n• Total driving time = \\(\\frac{1}{3} + \\frac{1}{6} + \\frac{2}{3} = \\frac{7}{6}\\) h. \n• Total dwell time = 3 × 10 min = 30 min = \\(\\frac{1}{2}\\) h. \n• Total time = \\(\\frac{7}{6} + \\frac{1}{2} = \\frac{7}{6} + \\frac{3}{6} = \\frac{10}{6} = \\frac{5}{3}\\) h. \n• Average speed = 60 ÷ \\(\\frac{5}{3}\\) = 60 × \\(\\frac{3}{5}\\) = 36 km/h. \n \nFinal Answer: 36 km/h"
},
{
"id": 6789,
"type": 1,
"question": "A driver travels 1 hour at 100 km/h, then 1 hour at 120 km/h, then 1 hour at 80 km/h, and takes a 1-hour meal break during the trip. What is the overall average speed?",
"answers": [
"75 km/h",
"80 km/h",
"72 km/h",
"90 km/h"
],
"correct_index": 0,
"solution": "Average speed = Total distance ÷ Total time.
\r\n• Distance at 100 km/h for 1 h: 100 km. \r\n• Distance at 120 km/h for 1 h: 120 km. \r\n• Distance at 80 km/h for 1 h: 80 km. \r\n• Total distance = 100 + 120 + 80 = 300 km. \r\n• Total time = 3 driving hours + 1 meal hour = 4 h. \r\n• Average speed = 300 ÷ 4 = 75 km/h. \r\n \r\nFinal Answer: 75 km/h"
},
{
"id": 6790,
"type": 1,
"question": "A car travels 180 km at 60 km/h, then 210 km at 70 km/h, then 240 km at 80 km/h. It stops 40 minutes after leg 1 and 20 minutes after leg 2. What is the overall average speed?",
"answers": [
"60 km/h",
"63 km/h",
"65 km/h",
"70 km/h"
],
"correct_index": 1,
"solution": "Average speed = Total distance ÷ Total time.
\r\n• Leg 1: 180 km at 60 km/h → 180 ÷ 60 = 3 h. \r\n• Leg 2: 210 km at 70 km/h → 210 ÷ 70 = 3 h. \r\n• Leg 3: 240 km at 80 km/h → 240 ÷ 80 = 3 h. \r\n• Total driving time = 3 + 3 + 3 = 9 h. \r\n• Total stop time = 40 min + 20 min = 60 min = 1 h. \r\n• Total distance = 180 + 210 + 240 = 630 km. \r\n• Total time = 9 + 1 = 10 h. \r\n• Average speed = 630 ÷ 10 = 63 km/h. \r\n \r\nFinal Answer: 63 km/h"
},
{
"id": 6791,
"type": 1,
"question": "A cyclist rides three equal 30-km segments at 30, 45, and 90 km/h. What is the trip’s average speed?",
"answers": [
"36 km/h",
"40 km/h",
"45 km/h",
"50 km/h"
],
"correct_index": 2,
"solution": "Average speed = Total distance ÷ Total time.
\n• Total distance = 3 × 30 = 90 km. \n• Time for each segment: \n• Segment 1: 30 ÷ 30 = 1 h \n• Segment 2: 30 ÷ 45 = \\(\\frac{2}{3}\\) h \n• Segment 3: 30 ÷ 90 = \\(\\frac{1}{3}\\) h \n• Total time = 1 + \\(\\frac{2}{3}\\) + \\(\\frac{1}{3}\\) = 2 h. \n• Average speed = 90 ÷ 2 = 45 km/h. \n \nFinal Answer: 45 km/h"
},
{
"id": 6792,
"type": 1,
"question": "A 300-km journey must average 75 km/h overall. The first 100 km are at 50 km/h and the next 50 km at 50 km/h. What constant speed is needed for the remaining distance?",
"answers": [
"120 km/h",
"140 km/h",
"150 km/h",
"160 km/h"
],
"correct_index": 2,
"solution": "Total time allowed = Total distance ÷ Target average speed.
\n• Time needed for 75 km/h average over 300 km: 300 ÷ 75 = 4 hours. \n• Time for first 100 km at 50 km/h: 100 ÷ 50 = 2 hours. \n• Time for next 50 km at 50 km/h: 50 ÷ 50 = 1 hour. \n• Time used so far: 2 + 1 = 3 hours. \n• Time remaining: 4 − 3 = 1 hour. \n• Distance remaining: 300 − 100 − 50 = 150 km. \n• Required speed: 150 ÷ 1 = 150 km/h.
\nFinal Answer: 150 km/h"
},
{
"id": 6795,
"type": 1,
"question": "A runner alternates 20 min at 12 km/h and 20 min at 18 km/h (two equal-time speeds) for a total of 120 min of running. There is one 60-min rest inserted anywhere. What is the overall average speed including the rest?",
"answers": [
"9 km/h",
"10 km/h",
"12 km/h",
"15 km/h"
],
"correct_index": 1,
"solution": "Running time = 120 min = 2 h, split equally between two speeds: 1 h each.
• Distance at 12 km/h = 12 × 1 = 12 km. • Distance at 18 km/h = 18 × 1 = 18 km. • Total running distance = 12 + 18 = 30 km.
Total time (including 60 min rest) = 120 + 60 = 180 min = 3 h. Overall average speed = 30 ÷ 3 = 10 km/h.
Final Answer: 10 km/h"
},
{
"id": 6796,
"type": 1,
"question": "A 60-km loop has three 20-km segments at 60, 30, and 20 km/h. At the end of each segment, the bus dwells 20 minutes. What is the average speed for the loop including all dwell times?",
"answers": [
"18 km/h",
"20 km/h",
"24 km/h",
"30 km/h"
],
"correct_index": 1,
"solution": "Average speed = Total distance ÷ Total time (including dwells).
\n• Segment 1: 20 km ÷ 60 km/h = \\( \\frac{1}{3} \\) h = 20 min travel + 20 min dwell = 40 min. \n• Segment 2: 20 km ÷ 30 km/h = \\( \\frac{2}{3} \\) h = 40 min travel + 20 min dwell = 60 min. \n• Segment 3: 20 km ÷ 20 km/h = 1 h = 60 min travel + 20 min dwell = 80 min. \n• Total time: 40 + 60 + 80 = 180 min = 3 hours. \n• Total distance: 60 km. \n• Average speed: 60 ÷ 3 = 20 km/h.
\nFinal Answer: 20 km/h"
},
{
"id": 6797,
"type": 1,
"question": "A car travels 60 km in 2 hours. What is its speed?",
"answers": [
"120 km/h",
"30 kmh",
"30 km/h",
"35 km/h"
],
"correct_index": 2,
"solution": "Speed = Distance ÷ Time.
• Distance = 60 km, Time = 2 h. • Speed = 60 ÷ 2 = 30 km/h.
Final Answer: 30 km/h"
},
{
"id": 6798,
"type": 1,
"question": "A cyclist goes 15 km in 30 minutes. What is his speed in km/h?",
"answers": [
"15 km/h",
"450 m/s",
"30 km/h",
"45 km/h"
],
"correct_index": 2,
"solution": "Convert minutes to hours, then find speed.
• 30 min = 0.5 h. • Speed = Distance ÷ Time = 15 ÷ 0.5 = 30 km/h.
Final Answer: 30 km/h"
},
{
"id": 6799,
"type": 1,
"question": "A runner covers 400 meters in 50 seconds. Find his speed in meters per second.",
"answers": [
"2000 m/s",
"10 m/s",
"8 m/s",
"12 m/s"
],
"correct_index": 2,
"solution": "Speed = Distance ÷ Time.
• Distance = 400 m, Time = 50 s. • Speed = 400 ÷ 50 = 8 m/s.
Final Answer: 8 m/s"
},
{
"id": 6800,
"type": 1,
"question": "A person walks 9 km at 3 km/h and then 6 km at 6 km/h. What is the average speed?",
"answers": [
"4.25 km/h",
"3.5 km/h",
"3.9 km/h",
"3.75 km/h"
],
"correct_index": 3,
"solution": "Average speed = Total distance ÷ Total time.
• First leg: 9 km at 3 km/h → time = 9 ÷ 3 = 3 h. • Second leg: 6 km at 6 km/h → time = 6 ÷ 6 = 1 h. • Total distance = 9 + 6 = 15 km. • Total time = 3 + 1 = 4 h. • Average speed = 15 ÷ 4 = 3.75 km/h.
Final Answer: 3.75 km/h"
},
{
"id": 6801,
"type": 1,
"question": "A car covers 120 km at 60 km/h and returns 120 km at 40 km/h. Find its average speed for the whole trip.",
"answers": [
"45 km/h",
"48 km/h",
"50 km/h",
"52 km/h"
],
"correct_index": 1,
"solution": "Average speed = Total distance ÷ Total time.
• Time to go: 120 ÷ 60 = 2 h. • Time to return: 120 ÷ 40 = 3 h. • Total distance = 120 + 120 = 240 km. • Total time = 2 + 3 = 5 h. • Average speed = 240 ÷ 5 = 48 km/h.
Final Answer: 48 km/h"
},
{
"id": 6803,
"type": 1,
"question": "A cyclist rides the first 30 km in 30 minutes and the next 30 km in 2 hours and 15 mins. What is his average speed?",
"answers": [
"20.7 km/h",
"21.50 km/h",
"21.82 km/h",
"21.95 km/h"
],
"correct_index": 2,
"solution": "Average speed = Total distance ÷ Total time.
• First leg: 30 km in 30 min = 0.5 h. • Second leg: 30 km in 2 h 15 min = 2.25 h. • Total distance = 30 + 30 = 60 km. • Total time = 0.5 + 2.25 = 2.75 h. • Average speed = 60 ÷ 2.75 ≈ 21.82 km/h.
Final Answer: \\(\\approx\\) 21.82 km/h"
},
{
"id": 6809,
"type": 1,
"question": "Mr Sulaiman left his home at 22.30 to drive to Kuala Lumpur, which is 462 km away.\r\nHe drove at an average speed of 84 km/h. What time did he reach Kuala Lumpur?",
"answers": [
"05.00 hours the following day",
"04.00 hours the following day",
"04.30 hours the following day",
"05.30 hours the following day"
],
"correct_index": 1,
"solution": "Time = Distance ÷ Speed.
• Time = 462 ÷ 84 = 5.5 h = 5 h 30 min.
Departure at 22:30. • 22:30 + 5 h = 03:30 (next day). • 03:30 + 30 min = 04:00 (next day).
Final Answer: 04.00 hours the following day"
},
{
"id": 6814,
"type": 1,
"question": "On a bus: 40 people average 25 years old. 10 passengers leave, 5 new passengers with average 30 years old board. New overall average is 26. What was the average age of the 10 who left?",
"answers": [
"20",
"22",
"24",
"26"
],
"correct_index": 2,
"solution": "Track total ages before and after the change.
• Before: 40 people, average 25 → total age = 40 × 25 = 1000. • After: 35 people, average 26 → total age = 35 × 26 = 910. • 5 new passengers, average 30 → they add 5 × 30 = 150.
Let x be the average age of the 10 who left. They took away 10x. 1000 − 10x + 150 = 910 1150 − 10x = 910 10x = 240 → x = 24.
Final Answer: 24"
},
{
"id": 6815,
"type": 1,
"question": "Eight numbers average 15. Removing the largest makes the average of the other seven = 12. What is the largest number?",
"answers": [
"32",
"34",
"36",
"38"
],
"correct_index": 2,
"solution": "Sum of all numbers = Average × Count.
• Sum of all 8 numbers = 8 × 15 = 120. • Sum of the 7 smaller numbers = 7 × 12 = 84. • Largest number = 120 − 84 = 36.
Final Answer: 36"
},
{
"id": 6816,
"type": 1,
"question": "Five consecutive odd numbers average 35. What’s the largest number?",
"answers": [
"37",
"39",
"41",
"43"
],
"correct_index": 1,
"solution": "Five consecutive odd numbers: let the middle (3rd) be the average = 35.
• The numbers: 31, 33, 35, 37, 39. • Largest number = 39.
Check: (31+33+35+37+39)/5 = 175/5 = 35. ✓
Final Answer: 39"
},
{
"id": 6817,
"type": 1,
"question": "12 players average 65 kg. Adding one player raises average to 66. What’s the new player’s weight?",
"answers": [
"74 kg",
"72 kg",
"76 kg",
"78 kg"
],
"correct_index": 3,
"solution": "Original total weight = Average × Count.
• 12 players: total = 12 × 65 = 780 kg. • 13 players: total = 13 × 66 = 858 kg. • New player's weight = 858 − 780 = 78 kg.
Final Answer: 78 kg"
},
{
"id": 6818,
"type": 1,
"question": "Four tests average 80. Student wants a 5-test average of 85. What must they score in the fifth?",
"answers": [
"95",
"100",
"105",
"110"
],
"correct_index": 2,
"solution": "Current total = Average × Count. Target total = Desired average × New count. Score needed = Target total − Current total.
Final Answer: 105"
},
{
"id": 6819,
"type": 1,
"question": "Groups average 70, 80, 90, with ratio 2:3:5. Find the combined average.",
"answers": [
"83",
"81",
"79",
"78"
],
"correct_index": 0,
"solution": "Weighted average: multiply each group's average by its ratio weight, then divide by total weight.
• Group 1: 70 × 2 = 140 • Group 2: 80 × 3 = 240 • Group 3: 90 × 5 = 450 • Sum = 140 + 240 + 450 = 830 • Total weight = 2 + 3 + 5 = 10 • Combined average = 830 ÷ 10 = 83.
Final Answer: 83"
},
{
"id": 6820,
"type": 1,
"question": "20 employees average 4,500 dollars in pay. A new manager earning 15,000 dollars joins. What’s the new average pay in dollars?",
"answers": [
"4500",
"5000",
"5500",
"5800"
],
"correct_index": 1,
"solution": "Total old pay = 20 × $4,500 = $90,000.
\r\nNew total pay = $90,000 + $15,000 = $105,000. \r\nNew number of people = 20 + 1 = 21.
\r\nNew average = $105,000 ÷ 21 = $5,000.
\r\nFinal Answer: $5,000\r\n"
},
{
"id": 6821,
"type": 1,
"question": "Ten numbers average 12. Replacing three numbers, 5,15,20, by a single number x makes the new average 13. Find \r\n𝑥.",
"answers": [
"22",
"24",
"26",
"28"
],
"correct_index": 1,
"solution": "Total of the 10 numbers = 10 × 12 = 120.
\r\nSum of the three removed numbers = 5 + 15 + 20 = 40. \r\nRemaining sum after removal = 120 − 40 = 80. \r\nNumber of values becomes 10 − 3 + 1 = 8.
\r\nNew average = 13, so 80 + x = 8 × 13 = 104. \r\nx = 104 − 80 = 24.
\r\nFinal Answer: 24\r\n"
},
{
"id": 6822,
"type": 1,
"question": "A set of 50 values has average 40. Removing two values changes the average to 39. The difference between those two removed values is 32. Find both values.",
"answers": [
"46 and 78",
"48 and 80",
"40 and 78",
"50 and 76"
],
"correct_index": 1,
"solution": "Original total = 50 × 40 = 2000.
\r\nAfter removing two values a and b, the count becomes 48 and average becomes 39: \r\n2000 − a − b = 48 × 39 = 1872. \r\nSo a + b = 2000 − 1872 = 128.
\r\nGiven a − b = 32: \r\n• a = (128 + 32) ÷ 2 = 80 \r\n• b = (128 − 32) ÷ 2 = 48
\r\nThe two removed values are 48 and 80. \r\nCheck: 48 + 80 = 128 and 80 − 48 = 32. ✓\r\n"
},
{
"id": 6823,
"type": 1,
"question": "Workshop A’s average is 70, Workshop B’s average is 85. Together the combined average is 79. B has 20 more people than A. How many in A and B?",
"answers": [
"20 and 40",
"50 and 70",
"35 and 55",
"40 and 60"
],
"correct_index": 3,
"solution": "Let A have a people and B have a + 20 people.
\r\nTotal score from A = 70a. Total score from B = 85(a + 20) = 85a + 1700. \r\nCombined total score = 70a + 85a + 1700 = 155a + 1700. \r\nCombined number of people = a + (a + 20) = 2a + 20.
\r\nA has 40 people, B has 40 + 20 = 60 people. \r\nCheck: (40×70 + 60×85) ÷ 100 = (2800+5100)÷100 = 79. ✓\r\n"
},
{
"id": 6824,
"type": 1,
"question": "A runner covers three equal distances. Speeds on legs 1 and 2 are 10 and 15 km/h. What speed on leg 3 achieves an overall average of 15 km/h?",
"answers": [
"20 km/h",
"30 km/h",
"35 km/h",
"40 km/h"
],
"correct_index": 1,
"solution": "Let each equal distance be d km.
\r\nTime for leg 1 = d ÷ 10 hours. \r\nTime for leg 2 = d ÷ 15 hours. \r\nTime for leg 3 = d ÷ v hours.
\r\nTotal distance = 3d. Total time = d/10 + d/15 + d/v. \r\nOverall average speed = 3d ÷ (d/10 + d/15 + d/v) = 15.
\r\nFinal Answer: 30 km/h\r\n"
},
{
"id": 6825,
"type": 1,
"question": "One hundred numbers average 50. The first 40 average 45, the next 30 average 55. What is the average of the final 30? Answer to 2 decimal places.",
"answers": [
"50.67",
"51.67",
"53.67",
"54.67"
],
"correct_index": 1,
"solution": "Total of all 100 numbers = 100 × 50 = 5000.
\r\nSum of first 40 = 40 × 45 = 1800. \r\nSum of next 30 = 30 × 55 = 1650.
\r\nSum of final 30 = 5000 − 1800 − 1650 = 1550. \r\nAverage of final 30 = 1550 ÷ 30 = 51.666... ≈ 51.67.
\r\nFinal Answer: 51.67\r\n"
},
{
"id": 6826,
"type": 1,
"question": "A dataset’s true average is 50. Due to one mis-recorded value, the reported average is 49.6. The wrong entry recorded 63 instead of 83. How many items are in the dataset?",
"answers": [
"30",
"40",
"50",
"55"
],
"correct_index": 2,
"solution": "Let n be the number of items in the dataset.
\r\nTrue total = 50 × n. \r\nReported total = 50n − 83 + 63 = 50n − 20.
\r\nReported average = (50n − 20) ÷ n = 49.6. \r\n50n − 20 = 49.6n. \r\n50n − 49.6n = 20. \r\n0.4n = 20, so n = 50.
\r\nFinal Answer: 50\r\n"
},
{
"id": 6827,
"type": 1,
"question": "Class A has n students averaging 60. Class B has m students averaging 90. 5 students, whose own average is \r\n92 are transferred from B to A. After the move, A’s average is 65 and B’s average is 88. Find original n and m.",
"answers": [
"25 and 12",
"27 and 10",
"26 and 8",
"26 and 10"
],
"correct_index": 1,
"solution": "Before transfer: \r\n• Class A: n students, total = 60n. \r\n• Class B: m students, total = 90m.
\r\nAfter 5 students (avg 92) move from B to A: \r\n• Class A new total = 60n + 5×92 = 60n + 460, count = n + 5. \r\n• Class B new total = 90m − 5×92 = 90m − 460, count = m − 5.
\r\nA's new average = 65: (60n + 460) ÷ (n + 5) = 65. \r\n60n + 460 = 65n + 325. \r\n135 = 5n, so n = 27.
\r\nB's new average = 88: (90m − 460) ÷ (m − 5) = 88. \r\n90m − 460 = 88m − 440. \r\n2m = 20, so m = 10.
\r\nFinal Answer: n = 27, m = 10\r\n"
},
{
"id": 6828,
"type": 1,
"question": "A student has 10 exam scores averaging 76. They retake some exams and raise each of those retaken scores by 8 points on average. After retakes, the overall average is 78.4. How many exams were retaken?",
"answers": [
"3",
"4",
"5",
"2"
],
"correct_index": 0,
"solution": "Original total = 10 × 76 = 760.
\r\nLet r = number of exams retaken. \r\nTotal increase from retakes = 8 × r. \r\nNew total = 760 + 8r.
\r\nNew average = (760 + 8r) ÷ 10 = 78.4. \r\n760 + 8r = 784. \r\n8r = 24, so r = 3.
\r\nFinal Answer: 3\r\n"
},
{
"id": 6829,
"type": 1,
"question": "A 60-item dataset averages 30. Group 1 (25 items) averages 24. Group 2 (15 items) averages 36. What must Group 3’s average be?",
"answers": [
"30",
"32",
"33",
"34"
],
"correct_index": 2,
"solution": "Total of all 60 items = 60 × 30 = 1800.
\r\nGroup 1 total = 25 × 24 = 600. \r\nGroup 2 total = 15 × 36 = 540.
\r\nFinal Answer: 33\r\n"
},
{
"id": 6830,
"type": 1,
"question": "A dataset has unknown size n and average 52. When one value x is replaced by ( x + 4), the average rises to 53.7. Find \r\n𝑛.",
"answers": [
"16",
"18",
"20",
"22"
],
"correct_index": 2,
"solution": "\r\nReplacing x with x + 4 increases the total sum by exactly 4.
\r\nOriginal average = 52, so original total = 52n. \r\nNew total = 52n + 4. \r\nNew average = (52n + 4) ÷ n = 53.7.
\r\nn is not an integer. The numbers in the question may be transcribed incorrectly — check the original source. If the average rise were 0.2 (instead of 1.7), then n = 4÷0.2 = 20, matching option C.
\r\nFinal Answer: n is approximately 2.35 (not an integer — likely a question error)\r\n"
},
{
"id": 6831,
"type": 1,
"question": "The average of n numbers is 40. Removing one number 28 increases the average to 41. Then adding a number y brings the average to 42 with the original count n. Find n and y.",
"answers": [
"12 and 50",
"14 and 56",
"13 and 56",
"13 and 54"
],
"correct_index": 3,
"solution": "Original total of n numbers = 40n.
\r\nAfter removing 28: \r\n• New total = 40n − 28, count = n − 1. \r\n• Average = (40n − 28) ÷ (n − 1) = 41. \r\n• 40n − 28 = 41n − 41. \r\n• 13 = n.
\r\nAfter adding y (back to original count n): \r\n• Total = 40n − 28 + y, count = n. \r\n• Average = (40n − 28 + y) ÷ n = 42. \r\n• 40(13) − 28 + y = 42(13). \r\n• 520 − 28 + y = 546. \r\n• 492 + y = 546, so y = 54.
\r\nFinal Answer: n = 13, y = 54\r\n"
},
{
"id": 6834,
"type": 1,
"question": "A library has 8 shelves. Each shelf has an average of 15 books. How many books are there in total?",
"answers": [
"100",
"110",
"120",
"80"
],
"correct_index": 2,
"solution": "Average = Total ÷ Count, so Total = Average × Count.
\r\nFinal Answer: 120\r\n"
},
{
"id": 6835,
"type": 1,
"question": "John spends an average of \\(\\$12\\) per day for 7 days. What is his total spending?",
"answers": [
"80",
"72",
"84",
"92"
],
"correct_index": 2,
"solution": "Total = Average × Number of days.
\n• Total spending = 12 × 7 = 84.
\nFinal Answer: 84"
},
{
"id": 6836,
"type": 1,
"question": "A basket has 10 mangoes. The average weight of each mango is 2 kg. What is the total weight?",
"answers": [
"20",
"12",
"24",
"22"
],
"correct_index": 0,
"solution": "Total weight = Average weight × Number of mangoes.
\r\nTotal weight = 10 × 2 kg = 20 kg.
\r\nFinal Answer: 20 kg\r\n"
},
{
"id": 6837,
"type": 1,
"question": "The average score of 5 students is 80. What is the total of their scores?",
"answers": [
"300",
"450",
"400",
"500"
],
"correct_index": 2,
"solution": "Total = Average × Count.
\r\nTotal of scores = 5 × 80 = 400.
\r\nFinal Answer: 400\r\n"
},
{
"id": 6838,
"type": 1,
"question": "Sarah has \\(\\$60\\) to spend equally over 5 days. How much does she spend on average per day?",
"answers": [
"10",
"12",
"14",
"13"
],
"correct_index": 1,
"solution": "Average = Total ÷ Number of days.