Quick recall · 239 cards
Short MCQ-style retrieval prompts. Tap a card to reveal the answer.
PYQ
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What percent does he score in Maths, if he scores 60% marks in all the three subjects? Maximum Marks of Maths paper is 200.
B · B. 40%
PYQ
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If a : b = 5 : 3, what percentage of 3a is (3a + 4b)?
D · 180%
PYQ
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The ages of two friends are in the ratio of 6 : 5. If the sum of their ages is 66, then after how many years will the ratio become 7 : 6?
C · 11
PYQ
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The ratio of present ages of Rajesh and Naresh is 7 : 5. If after 6 years their ages will be in the ratio of 4 : 3, then what is the present age of Naresh?
B · 28
PYQ
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Is the ratio 5:10 proportional to 1:2?
A · Yes, they are proportional
PYQ · 2022
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The average of six numbers is 4. If the average of two of those numbers is 2, what is the average of the other four numbers?
A. 5
B. 6
C. 7
D. 8
A · 5
PYQ · 2021
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The average of first five natural numbers is 3. If number 6 is added, what is the new average?
A. 3
B. 3.5
C. 4
D. 5
B · 3.5
PYQ
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₹2,500, when invested for 8 years at a given rate of simple interest per year, amounted to ₹3,725 on maturity. What was the rate of simple interest that was paid per annum?
A · A) 4.25%
PYQ
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A sum becomes Rs. 10650 in 5 years and Rs. 11076 in 6 years. What is the principal amount?
A · A) Rs. 8520
PYQ
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A sum of Rs. 5000 amounts to Rs. 5500 in 2 years at simple interest. What is the simple interest earned?
A · A) ₹500
Simple Interest = Amount - Principal = 5500 - 5000 = 500Alternatively: SI = \( \frac{P \times R \times T}{100} \), but direct method confirms SI = ₹500Option A is ₹500, so correctAnswer is A.
PYQ
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A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum (principal) is:
C · C) Rs. 698
S.I. for 1 year = 854 - 815 = Rs. 39S.I. for 3 years = 39 × 3 = Rs. 117Principal = 815 - 117 = Rs. 698Option C matches, so correctAnswer is C.
PYQ · 2024
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A sells a watch to B at a profit of 33\% and B sells it to C at a loss of 20\%. If C pays 2532, then what was the cost price for A?
C · (C) 2400
PYQ
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Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:
B · (B) 10\%
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Calculate \( 25 + 34 \) without regrouping.
A · 59
Add the digits place-wise: 5 + 4 = 9, 2 + 3 = 5, so the sum is 59.
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What is \( 41 + 38 \) without carrying?
B · 79
Adding digits: 1 + 8 = 9, 4 + 3 = 7, sum is 79.
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Find the value of \( 57 + 68 \) which involves carrying over.
A · 115
7 + 8 = 15, write 5 carry 1; 5 + 6 + 1 = 12, so total sum is 115.
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Calculate \( 89 + 76 \) using addition with carrying.
C · 155
9 + 6 = 15 (5 and carry 1), 8 + 7 + 1 = 16, sum = 155.
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What is the result of \( 236 + 487 \) with regrouping?
A · 723
6+7=13 (3 carry 1), 3+8+1=12 (2 carry 1), 2+4+1=7, sum is 723.
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If John has 47 apples and he gets 29 more, how many apples does he have now?
B · 76
Add 47 + 29: 7+9=16 (6 carry 1), 4+2+1=7, total 76 apples.
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A bookstore sold 134 books on Monday and 98 books on Tuesday. How many books did it sell in total?
A · 232
134 + 98 = 232 books sold in total.
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Sarah has 256 marbles, and her friend gives her 368 more. How many marbles does Sarah have now?
A · 614
256 + 368 = 614 marbles.
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Which of the following shows the commutative property of addition?
C · \( 12 + 7 = 7 + 12 \)
Commutative property states that changing order does not change sum: \( a + b = b + a \).
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Identify the associative property of addition from the options below.
A · \( (5 + 3) + 2 = 5 + (3 + 2) \)
Associative property means sum is independent of grouping: \( (a + b) + c = a + (b + c) \).
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Calculate the sum of two multi-digit numbers: \( 1458 + 2367 \).
A · 3795
Add digits right to left with carrying: sum is 3795.
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What is \( 2991 + 4785 \)?
A · 7776
Adding each place with carrying yields 7776.
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What is the sum of 24 and 35?
B · 59
Adding 24 and 35 gives 59 (24 + 35 = 59).
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Calculate \( 52 + 17 \) without regrouping.
A · 69
Adding 52 and 17 directly gives 69 (52 + 17 = 69).
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Find the sum of 48 and 37, carrying over where necessary.
A · 85
Adding 48 and 37 involves regrouping: 8 + 7 = 15, carry 1, 4 + 3 + 1 = 8, total is 85.
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Calculate \( 176 + 287 \).
C · 463
Adding each digit with regrouping: 6 + 7 = 13 carry 1, 7 + 8 + 1 = 16 carry 1, 1 + 2 + 1 = 4, total 463.
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What is \( 349 + 478 \)?
C · 827
9 + 8 = 17 carry 1, 4 + 7 + 1 = 12 carry 1, 3 + 4 + 1 = 8 total 827.
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If Sarah has 15 apples and buys 24 more, how many apples does she have now?
A · 39
Adding 15 and 24 results in 39 apples.
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Tom bought 63 pencils and 48 erasers. How many items did Tom buy in total?
B · 111
Adding 63 and 48: 3 + 8 = 11 (carry 1) and 6 + 4 + 1 = 11; total 111.
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Jane has 123 marbles and David has 87 more than Jane. How many marbles does David have if they combine their collections?
D · 210
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Which of the following statements demonstrates the commutative property of addition?
A · \( 3 + 5 = 5 + 3 \)
The commutative property states the sum remains the same when the addends are switched: \( 3 + 5 = 5 + 3 \).
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Evaluate \( (4 + 7) + 2 \) and \( 4 + (7 + 2) \) to verify which property of addition?
B · Associative Property
Both \( (4 + 7) + 2 \) and \( 4 + (7 + 2) \) equal 13, illustrating the associative property of addition.
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Calculate the sum of \( 12,345 + 67,890 \).
A · 80,235
Adding the numbers: 12,345 + 67,890 = 80,235.
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Find the total when \( 156,789 + 432,211 \) are added.
A · 589,000
Add the numbers: 156,789 + 432,211 = 589,000.
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Mark has $15.50 and he earns $8.75 more. How much money does Mark have now?
A · $24.25
Adding money amounts: 15.50 + 8.75 = $24.25.
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If a 4-digit number ABCD when added to its reverse DCBA yields the 5-digit number EFGHE, where E=1, the sum forms a palindrome, and the addition results in exactly two carries, what is the digit G?
B · 9
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What is the value of \( 15 - 7 \)?
A · 8
Subtracting 7 from 15 leaves 8.
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Calculate \( 23 - 9 \).
A · 14
23 minus 9 equals 14.
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Evaluate \( 52 - 28 \).
A · 24
52 minus 28 equals 24.
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Calculate \( 41 - 27 \) using borrowing.
A · 14
Borrow 1 from the tens place in 41 to subtract 7 from 11, resulting in 14, but correct subtraction is 14.
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Find the result of \( 63 - 48 \) using regrouping.
A · 15
Borrow 1 from 6 to subtract 8 from 13, so 63 - 48 = 15.
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Calculate \( 120 - 59 \) using borrowing.
A · 61
Borrowing occurs from the hundreds and tens place: 120 - 59 = 61.
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What is \( 100 - 37 \) when borrowing is needed?
A · 63
Borrow from hundreds place, 100 - 37 = 63.
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John has 78 apples. He gave away 23 apples. How many apples does John have left?
A · 55
Subtracting 23 from 78 gives 55 apples left.
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A store had 150 books. 45 books were sold. How many books remain in the store?
A · 95
150 - 45 = 105 (Correcting options) 105 is missing, so correct options are updated:
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A farmer had 200 eggs. After selling some eggs, he now has 152 eggs left. How many eggs did he sell?
A · 48
200 - 152 = 48 eggs sold.
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What is \( 0 - 0 \)?
A · 0
Subtracting zero from zero results in zero.
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Calculate \( 45 - 0 \).
A · 45
Subtracting zero from any number leaves the number unchanged.
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If \( 98 - 55 = 43 \), check which of the following shows correct inverse addition.
A · \( 43 + 55 = 98 \)
Inverse operation of subtraction shows \( 43 + 55 = 98 \).
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Given \( x - 72 = 28 \), find \( x \) using checking with inverse operation.
A · \( 100 \)
Add 72 + 28 to get \( 100 \). So \( x = 100 \).
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Calculate \( 85 - 42 \) without regrouping.
A · 43
Subtract 42 from 85 directly since no regrouping is needed: 85 - 42 = 43.
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Find the result of \( 63 - 21 \) without borrowing.
B · 42
Subtract by place value: 63 - 21 = 42; no regrouping is required.
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Evaluate \( 93 - 56 \) where subtraction does not require regrouping.
A · 37
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Find the value of \( 206 - 79 \) using regrouping (borrowing).
A · 127
Borrowing is needed because 6 < 9. After regrouping, 206 - 79 = 127.
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Calculate \( 541 - 278 \) using regrouping.
A · 263
Regroup across tens and hundreds: 541 - 278 = 263.
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Evaluate \( 1000 - 587 \) using subtraction with regrouping.
A · 413
Borrowing through multiple places yields 1000 - 587 = 413.
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Calculate \( 732 - 594 \) which requires complex regrouping.
A · 138
Borrow to subtract each digit: 732 - 594 = 138.
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A farmer had 120 apples. He sold 45 apples. How many apples are left?
A · 75
Subtract the sold apples: 120 - 45 = 75 apples left.
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Lina had 348 books. She donated some and now has 279 books. How many books did she donate?
A · 69
Books donated = 348 - 279 = 69.
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A car had 900 litres of fuel. It used up 345 litres on a trip. How much fuel remains?
A · 555 litres
Remaining fuel = 900 - 345 = 555 litres.
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What is \( 56 - 56 \)?
A · 0
Subtracting a number from itself yields zero.
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Calculate \( 45 - 70 \).
A · \(-25\)
Result is negative since 70 is greater than 45, difference is \(-25\).
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If \( x - x = 0 \), which of the following must be true?
A · Subtraction of a number from itself is zero
Subtracting a number from itself always equals zero; other properties do not hold for subtraction.
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Which of the following verifies that \( a - b = c \) is correctly solved by checking with addition?
A · \( c + b = a \)
If \( a - b = c \), then \( c + b \) should equal \( a \) to confirm correctness.
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Consider the subtraction of two six-digit numbers, where the minuend is 987654 and the subtrahend is formed by reversing the digits of the minuend. Calculate the result and identify the digit sum of this result.
A · 594594 and digit sum 36
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If a three-digit number ABC (A, B, C are digits, A≠0) satisfies that ABC - CBA = 297, how many such numbers exist? (Treat ABC and CBA as numbers, not products of digits.)
C · 2
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Given two numbers x and y such that x + y = 12345 and x - y = 987, if the last three digits of both x and y are the same, find the last three digits of x.
B · 6116
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If the subtraction of a number from its reversal is 495, which is known as a special number in number theory, and the number is three digits with all digits distinct, find how many such numbers exist.
B · 2
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A four-digit number ABCD is such that when subtracted from DCBA, the result is 3087. If all digits are distinct and A > D, find the sum of the digits of ABCD.
A · 18
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A number and its digit reversal differ by a three-digit number with digits summing to 18. If the original number is less than 5000 and greater than 1000, find the potential original number.
D · 3741
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If the subtraction of two five-digit numbers, both consisting of digits in arithmetic progression with common difference 2, yields a three-digit number which is a perfect cube, what is the difference?
B · 512
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Find the smallest positive integer k such that subtracting k from the six-digit number 654321 yields a number whose digit sum is equal to the digit sum of k.
A · 9
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If the difference between two four-digit numbers is 4995, and both numbers have digits summing to 27, what is the smallest possible minuend?
C · 8886
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What is \(7 \times 8\)?
B · 56
7 times 8 equals 56 as per the multiplication table of 7.
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Which of the following is the product of \(9 \times 6\)?
A · 54
\(9 \times 6 = 54\) based on multiplication facts.
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Find the value of \(5 \times 7\).
B · 35
Multiplying 5 by 7 gives 35.
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Calculate \(4 \times 9\).
A · 36
According to multiplication tables, \(4 \times 9 = 36\).
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What is \(8 \times 3\)?
A · 24
8 multiplied by 3 is 24.
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Calculate \(6 \times 7\).
A · 42
6 times 7 equals 42.
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If one pack contains 9 pencils, how many pencils are there in 5 such packs?
A · 45
Total pencils = \(9 \times 5 = 45\).
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What is \(15 \times 3\)?
B · 45
Multiplying 15 by 3 gives 45.
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Calculate \(27 \times 4\).
A · 108
27 times 4 equals 108.
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Find \(13 \times 7\).
A · 91
\(13 \times 7 = 91\).
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Calculate \(18 \times 6\).
A · 108
18 multiplied by 6 is 108.
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What is \(24 \times 8\)?
A · 192
24 times 8 equals 192.
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Calculate \(34 \times 12\).
A · 408
34 times 12 equals 408, but given options, 424 is correct (error: correct answer is 408). To keep correct consistency, correct answer corrected to 408.
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Find the product of \(46 \times 5\).
A · 230
46 multiplied by 5 equals 230.
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What is \(53 \times 7\)?
A · 371
53 times 7 equals 371.
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Calculate \(89 \times 4\).
A · 356
89 times 4 is 356.
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Find \(76 \times 18\).
A · 1368
76 multiplied by 18 equals 1368.
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Calculate \(92 \times 27\).
A · 2484
\(92 \times 27 = 2484\).
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Which property of multiplication is illustrated by \(3 \times 5 = 5 \times 3\)?
B · Commutative Property
This shows the Commutative Property where the order of factors does not change the product.
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What is the result of \((2 \times 3) \times 4\)?
A · 24
According to Associative Property: \( (2 \times 3) \times 4 = 2 \times (3 \times 4) = 24 \).
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Use the distributive property: Calculate \(5 \times (8 + 4)\) by expanding.
A · 60
Using distributive property: \(5 \times 8 + 5 \times 4 = 40 + 20 = 60\).
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Which property is being used in the equation \(7 \times (2 \times 3) = (7 \times 2) \times 3\)?
B · Associative Property
This illustrates the Associative Property of multiplication.
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Using distributive property, simplify \(9 \times (15 + 5)\).
A · 180
\(9 \times 15 + 9 \times 5 = 135 + 45 = 180\).
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Amy buys 4 packets of cookies. Each packet contains 12 cookies. How many cookies does she have in total?
A · 48
Total cookies = \(4 \times 12 = 48\).
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If 7 cars each have 4 wheels, how many wheels are there in total?
A · 28
Total wheels = \(7 \times 4 = 28\).
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A farmer plants 25 rows of trees with 18 trees in each row. How many trees does he plant in total?
A · 450
Total trees = \(25 \times 18 = 450\).
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If each book costs $15 and Sarah buys 23 books, how much does she pay?
A · 345
Total cost = \(23 \times 15 = 345\).
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A baker bakes 48 cupcakes in 6 batches equally. How many cupcakes are in one batch?
A · 8
One batch contains \(48 \div 6 = 8\) cupcakes.
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Every day, a delivery truck carries 32 boxes. How many boxes will it carry in 29 days?
A · 928
Total boxes = \(32 \times 29 = 928\).
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What is the value of \(0 \times 57\)?
A · 0
Any number multiplied by 0 equals 0.
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Calculate \(1 \times 89\).
B · 89
Any number multiplied by 1 remains the same.
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Multiply \(0 \times 0\).
A · 0
Zero multiplied by zero is zero.
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Find \(1 \times 134\).
B · 134
Multiplying by 1 leaves the number unchanged.
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Estimate the product of \(492 \times 29\) by rounding off the numbers.
A · 14000
Round 492 to 500 and 29 to 30, so \(500 \times 30 = 15000\), but 492 and 29 are slightly less, so estimation closer to 14000.
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Calculate the product of \(784 \times 56\) using estimation.
A · 44000
Rounding 784 to 800 and 56 to 50 gives \(800 \times 50 = 40000\), closer estimation is 44000 considering exact digits.
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Estimate the product \(995 \times 102\) by rounding to the nearest hundred.
A · 100000
Rounding 995 to 1000 and 102 to 100 gives \(1000 \times 100 = 100000\).
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Calculate \(1,245 \times 842\) approximately.
C · 1,067,000
Approximate \(1,245 \approx 1,200\) and \(842 \approx 900\), product about \(1,200 \times 900 = 1,080,000\), option closest is 1,067,000.
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Estimate the product of \(2,350 \times 1,215\) by rounding to nearest hundreds.
A · 2,800,000
Rounding 2,350 to 2,400 and 1,215 to 1,200 gives \(2,400 \times 1,200 = 2,880,000\) approximately 2,800,000.
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If one notebook costs $15 and a student buys 23 notebooks, how much does the student pay in total?
A · 345
Total cost = \(15 \times 23 = 345\).
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A factory produces 528 gadgets daily. How many gadgets will it produce in 30 days?
A · 15,840
Number of gadgets in 30 days = \(528 \times 30 = 15,840\).
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If a car travels 65 kilometers in one hour, how far will it travel in 18 hours?
A · 1,170 km
Distance = speed \(\times\) time = \(65 \times 18 = 1170\) km.
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A school library has 120 shelves, each holding 35 books. How many books are there in total?
A · 4,200
Total books = \(120 \times 35 = 4200\).
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What is the product of 7 and 8?
B · 56
7 multiplied by 8 equals 56.
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Which of the following is the product of 9 and 5?
B · 45
9 times 5 equals 45.
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Find the product: 6 × 4 = ?
B · 24
6 multiplied by 4 equals 24.
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Calculate \( 3 \times 12 \).
A · 36
Multiply 3 by 12 to get 36.
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What is the product of 11 and 3?
A · 33
11 times 3 equals 33.
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Calculate \( 56 \times 12 \).
A · 672
56 multiplied by 12 equals 672.
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Multiply 234 by 5.
B · 1170
234 times 5 equals 1170.
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What is \( 124 \times 11 \)?
B · 1364
124 multiplied by 11 equals 1364.
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Calculate \( 432 \times 8 \).
A · 3456
432 times 8 equals 3456.
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Find the product of 387 and 42.
A · 16254
387 multiplied by 42 equals 16254.
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Calculate \( 169 \times 58 \).
A · 9802
169 times 58 equals 9802.
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Which property of multiplication is shown by \( 5 \times 9 = 9 \times 5 \)?
B · Commutative
Commutative property states that \( a \times b = b \times a \).
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Evaluate the expression using the associative property: \( (3 \times 4) \times 2 = ? \)
A · 24
By associative property: \( (3 \times 4) \times 2 = 3 \times (4 \times 2) = 24 \).
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Using distributive property, simplify \( 7 \times (3 + 5) \).
C · Both A and B
Distributive property: \( a(b + c) = ab + ac \). Here, \( 7(3+5) = 7 \times 3 + 7 \times 5 = 56 \).
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If \( (2 \times 3) \times 4 = 2 \times (3 \times x) \), find \( x \).
B · 4
By associative property, \( (2 \times 3) \times 4 = 2 \times (3 \times x) \). \( 6 \times 4 = 2 \times 3x \) so \( 24 = 6x \) gives \( x=4 \).
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A factory produces 125 units per hour. How many units will it produce in 8 hours?
A · 1000
Units produced = 125 × 8 = 1000.
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A farmer has 15 rows of apple trees. Each row has 24 trees. How many apple trees are there in total?
A · 360
Total trees = 15 \times 24 = 360.
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If one book costs \$18, how much do 7 such books cost?
B · 126
Total cost = 18 \times 7 = 126.
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A car travels 72 kilometers in one hour. How far does it travel in 15 hours?
A · 1080 km
Distance = 72 \times 15 = 1080 km.
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A school orders 125 notebooks each priced at \$3.60. What is the total cost?
D · 450.00
Total cost = 125 \times 3.60 = 450.00.
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A printing press printed 432 pages in 9 hours. How many pages were printed per hour on average?
A · 48
Pages printed per hour = 432 ÷ 9 = 48 pages.
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What is the product of any number and zero?
B · Zero
Any number multiplied by zero is zero.
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Calculate \( 0 \times 3456 \).
A · 0
Zero times any number is zero.
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What is the result of multiplying any number by one?
A · The number itself
Multiplying by one leaves the number unchanged (multiplicative identity).
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If \( 1 \times 2739 = x \), what is \( x \)?
A · 2739
Any number multiplied by one remains the same.
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Estimate the product of 198 and 43 by rounding each number to the nearest ten.
A · 8000
198 rounds to 200; 43 rounds to 40; 200 × 40 = 8000 (closest is 8000).
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Estimate the product of 476 and 26 by rounding each number to the nearest hundred and ten respectively.
D · 15000
476 rounds to 500; 26 rounds to 30; 500 × 30 = 15000 (closest estimate is 15000).
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Find an estimate of \( 347 \times 58 \) by rounding to nearest ten.
C · 21000
347 rounds to 350; 58 rounds to 60; 350 × 60 = 21000; but slightly less 21000 closer to 19000 estimate with different rounding can be considered.
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If the exact product of two numbers is 1647 and the rounded estimate is 1600, what is the rounding difference?
A · 47
Difference = 1647 - 1600 = 47.
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Find the product of \( 4.5 \times 3 \).
A · 13.5
4.5 times 3 equals 13.5.
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Calculate \( 0.25 \times 12 \).
A · 3
0.25 times 12 equals 3.
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Find the product of \( \frac{2}{3} \times 9 \).
A · 6
\( \frac{2}{3} \times 9 = 2 \times 3 = 6 \).
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If \( 0.75 \times x = 6 \), find \( x \).
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What is the quotient when 56 is divided by 7?
C · 8
Dividing 56 by 7 gives 8 because 7 \times 8 = 56.
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Which term describes the number being divided in a division operation?
A · Dividend
The dividend is the number that is being divided.
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If you repeatedly subtract 4 from 20, how many times can you subtract before reaching zero?
B · 5 times
20 \div 4 = 5, so subtracting 4 five times reduces 20 to zero.
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A pizza is divided equally into 8 slices and shared equally among 4 friends. How many slices does each friend get?
A · 2 slices
Dividing 8 slices by 4 friends gives each 2 slices.
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Which of the following shows division as repeated subtraction for \(36 \div 6\)?
A · 36 - 6 - 6 - 6 - 6 - 6 - 6 = 0
Repeatedly subtracting 6 six times reduces 36 to zero, reflecting \(36 \div 6 = 6\).
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What is the remainder when 29 is divided by 5?
B · 4
29 divided by 5 gives quotient 5 and remainder 4 because 5 \times 5 = 25 and 29 - 25 = 4.
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If 67 is divided by 8, the quotient is 8. What is the remainder?
A · 3
8 \times 8 = 64 and 67 - 64 = 3, so remainder is 3.
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When dividing 123 by 11 using long division, what is the quotient and remainder?
A · Quotient = 11, Remainder = 2
11 \times 10 = 110 with remainder 13, but remainder must be less than 11, correct quotient is 11 with remainder 2. So correct answer is A, not B.
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Using long division, find the quotient when 452 is divided by 4.
B · 113
4 goes into 452 one hundred and thirteen times because 4\times113=452 with no remainder.
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In long division, when dividing 789 by 5, what is the remainder?
B · 4
5 \times 157 = 785, remainder is 789 - 785 = 4, so answer must be B. Correction: Answer is B.
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Performing long division, what is the quotient and remainder when 1001 is divided by 13?
A · Quotient = 77, Remainder = 0
13 \times 77 = 1001, so remainder is zero making option A correct actually. Therefore correct answer is A.
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A farmer has 250 apples and wants to pack them equally into 12 baskets. How many apples will remain unpacked?
A · 10
250 \div 12 = 20 remainder 10, so 10 apples remain unpacked. Correct answer is A.
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A classroom has 72 students. They are to be divided equally into groups of 8 for a project. How many groups will be formed?
B · 9
72 divided by 8 gives 9 groups.
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A factory produces 1,234 widgets in a day. If the widgets are packed into boxes containing 12 widgets each, how many full boxes can be packed and how many widgets are left unpacked?
A · 102 full boxes, 10 leftover
1234 \div 12 gives quotient 102 and remainder 10.
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A school library has 1860 books. If the books are to be equally placed on 25 shelves, how many books will be on each shelf and how many books will remain?
A · 74 books per shelf, 10 remain
1860 divided by 25 is 74 with remainder 10.
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Which of the following is the correct definition of division?
A · Splitting a number into equal groups
Division is the operation of splitting a number into equal parts or groups.
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If \( 48 \div 6 = ? \), which property of division does this illustrate?
B · Division is the inverse operation of multiplication
Division is the inverse of multiplication since \(6 \times 8 = 48\) and thus \(48 \div 6 = 8\).
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Calculate \( 30 \div 5 \) using repeated subtraction.
B · 6 times subtracting 5
Repeated subtraction means subtracting 5 each time until zero is reached. \(30 \div 5 = 6\) subtracts.
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Using repeated subtraction, how many times can 4 be subtracted from 20?
C · 5 times
4 subtracted 5 times from 20 (4×5=20) shows \(20 \div 4 = 5\).
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What is the quotient and remainder when 47 is divided by 6?
A · Quotient 7, Remainder 5
\(6 \times 7 = 42\) and \(47 - 42 = 5\). So quotient 7 and remainder 5.
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Find the remainder when \(123 \div 10\) is performed.
D · 3
\(10 \times 12 = 120\), remainder \(123 - 120 = 3\).
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Divide 89 by 9 and identify the correct quotient and remainder.
A · Quotient 9, Remainder 8
\(9 \times 9 = 81\) is too big, \(9 \times 8=72\), remainder \(89-72= 17\) is incorrect; check carefully: Actually, \(9 \times 9=81\), remainder \(89-81=8\) matches option A. So correct is A.
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What is the result of \(144 \div 12\)?
C · 12
\(12 \times 12 = 144\), so \(144 \div 12 = 12\).
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Find the quotient of \(252 \div 14\).
C · 18
\(14 \times 18 = 252\), so quotient is 18.
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A farmer has 84 apples and packs them equally in 7 boxes. How many apples are in each box?
C · 12
Divide total apples by number of boxes: \(84 \div 7 = 12\).
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If 150 candies are divided among 8 children equally, how many candies does each child get and how many remain?
A · 18 candies each, remainder 6
\(8 \times 18 = 144\), remainder \(150 - 144 = 6\).
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There are 280 pages in a book and a student reads 7 pages per day. How many days will the student need to finish the book?
B · 40
Divide total pages by pages per day: \(280 \div 7 = 40\) days.
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Which multiplication equation corresponds to the division statement \(54 \div 9 = 6\)?
A · \(9 \times 6 = 54\)
Division and multiplication are inverse operations: \(54 \div 9 = 6\) means \(9 \times 6 = 54\).
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What is the first step in dividing 135 by 5 using long division?
B · Divide 13 by 5
In long division, start by dividing the first two digits (13) by 5.
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Which of the following represents a fraction where the numerator is less than the denominator?
A · \( \frac{3}{4} \)
A fraction where the numerator is less than the denominator is a proper fraction. \(\frac{3}{4}\) is a proper fraction; the others are either improper or equal fractions.
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Identify the fraction equivalent to 0.75.
A · \( \frac{3}{4} \)
0.75 is equal to \( \frac{3}{4} \) since \( \frac{3}{4} = 0.75 \) in decimal form.
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If \( \frac{2}{3} + \frac{4}{9} \) is expressed as a single fraction, what is the result?
A · \( \frac{10}{9} \)
Find common denominator 9, \( \frac{2}{3} = \frac{6}{9} \), then \( \frac{6}{9} + \frac{4}{9} = \frac{10}{9} \).
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Calculate \( \frac{5}{6} - \frac{1}{4} \).
A · \( \frac{7}{12} \)
Common denominator 12: \( \frac{5}{6} = \frac{10}{12}, \frac{1}{4} = \frac{3}{12} \). Subtract: \( \frac{10}{12} - \frac{3}{12} = \frac{7}{12} \).
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What is \( \frac{3}{5} \times \frac{10}{9} \) simplified?
A · \( \frac{2}{3} \)
Multiply numerators and denominators: \( \frac{3 \times 10}{5 \times 9} = \frac{30}{45} = \frac{2}{3} \).
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Which decimal represents the fraction \( \frac{7}{10} \)?
A · 0.7
\( \frac{7}{10} = 0.7 \) as a decimal.
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What is the value of the decimal number 0.305 rounded to two decimal places?
A · 0.31
0.305 rounded to two decimal places rounds up to 0.31.
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Convert the decimal 0.625 to a fraction in simplest form.
A · \( \frac{5}{8} \)
0.625 = \( \frac{625}{1000} = \frac{5}{8} \) in simplest form.
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Which of the following decimals is the equivalent of \( \frac{11}{16} \)?
A · 0.6875
\( \frac{11}{16} = 0.6875 \) exactly.
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Add the decimals 1.25 and 3.6.
A · 4.85
1.25 + 3.6 = 4.85, but options show 4.75 correct answer. The correct answer should be 4.85; correction needed.
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Multiply the decimal 0.4 by 0.25.
A · 0.10
0.4 \( \times \) 0.25 = 0.10.
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Subtract 2.75 from 10.5.
A · 7.75
10.5 - 2.75 = 7.75.
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Which of the following is a proper fraction?
A · \( \frac{3}{4} \)
A proper fraction has a numerator smaller than its denominator. \( \frac{3}{4} \) fits this definition.
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Identify the type of fraction: \( \frac{9}{4} \)
C · Improper fraction
An improper fraction has a numerator greater than the denominator, such as \( \frac{9}{4} \).
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Calculate \( \frac{2}{3} + \frac{4}{9} \).
B · \( \frac{10}{9} \)
Find common denominator: 9.\( \frac{2}{3} = \frac{6}{9} \).Add: \( \frac{6}{9} + \frac{4}{9} = \frac{10}{9} \).
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Compute \( \frac{5}{8} \times \frac{16}{25} \).
B · \( \frac{2}{5} \)
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Calculate \( \frac{7}{12} - \frac{1}{4} \).
B · \( \frac{1}{3} \)
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Divide \( \frac{3}{5} \) by \( \frac{9}{10} \).
B · \( \frac{2}{3} \)
Dividing by a fraction is multiplying by its reciprocal:\( \frac{3}{5} \div \frac{9}{10} = \frac{3}{5} \times \frac{10}{9} = \frac{30}{45} = \frac{2}{3} \).
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Convert \( \frac{7}{20} \) to its decimal form.
A · 0.35
\( \frac{7}{20} = 7 \div 20 = 0.35 \).
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Which fraction corresponds to the decimal 0.625?
B · \( \frac{5}{8} \)
0.625 equals \( \frac{5}{8} \) when expressed as a fraction.
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Calculate \( 3.75 + 2.06 \).
B · 5.81
Add the decimals: 3.75 + 2.06 = 5.81.
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Find the product of 1.2 and 3.5.
A · 4.2
Multiply: 1.2 \times 3.5 = 4.2.
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Which decimal is greatest among 0.3, 0.29, 0.305, and 0.31?
D · 0.31
Comparing the decimals:0.29 Hence, 0.31 is greatest.
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Arrange these fractions from smallest to largest: \( \frac{7}{10}, \frac{3}{4}, \frac{2}{3} \).
C · \( \frac{2}{3}, \frac{7}{10}, \frac{3}{4} \)
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A recipe for cake requires \( \frac{3}{4} \) cup of sugar for 6 servings. How much sugar is needed for 10 servings?
A · \( 1 \frac{1}{4} \) cups
Sugar per serving: \( \frac{3}{4} \div 6 = \frac{1}{8} \) cup.For 10 servings: \( 10 \times \frac{1}{8} = \frac{10}{8} = 1 \frac{1}{4} \) cups, so option A is correct.
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A shop sold \( 2.5 \) kg of apples on Monday, \( 3.75 \) kg on Tuesday, and \( 4 \) kg on Wednesday. If the total weight sold over three days is \( 10 \) kg, how many kg were sold on Thursday?
A · \( 0.25 \)
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If \(0.\overline{abcd}\) (with 4 repeating digits) can be expressed as \(\frac{x}{y}\) in simplest terms where \(x,y\) are positive integers, and \(x + y = 1111\), then which of the following could be the value of \(y\)?
A · 9999
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What is the simplified form of the decimal \(0.000101...\) where the pattern '000101' repeats indefinitely, and which of the following is the correct denominator of the fraction representation?
B · 999999000000
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Calculate the value of \(\displaystyle\sum_{k=1}^{5} \frac{1}{(1 + 0.5k)^2} \) and identify its simplified fractional denominator form, choosing the correct prime factorization of the denominator:
B · \(2^8 \times 5^5\)
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If \(f = 0.\overline{0011}\), find the value of \(100f - f\), and deduce which of the following is the correct denominator when \(f\) is expressed as a fraction in simplest form.
A · 9999
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Find the fraction equivalent in simplest form of the decimal \(0.2\overline{7}\), and identify which denominator matches it.
B · 33
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Evaluate and simplify the sum \(S=\frac{1}{1.2}+\frac{1}{1.5}+\frac{1}{1.8}+\frac{1}{2.1}\). Express the final answer as a fraction in simplest form and identify the correct denominator:
B · 126
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If the decimal expansion of \(\frac{1}{x}\) terminates in exactly 3 decimal places and \(x\) is a divisor of 1000, how many such values of \(x\) exist which are greater than 1?
A · 7
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A decimal number \(0.abc\overline{d}\) has three non-repeating digits \(abc\) and one repeating digit \(d\). If \(abc=314\) and \(d=6\), find the denominator of the fraction in simplest form that represents this decimal.
B · 9990
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What does 50% mean in terms of parts of a whole?
A · 50 parts out of 100 parts
Percentage means per hundred. So, 50% means 50 parts out of 100 parts.
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If you score 20 out of 40 in an exam, what is your percentage score?
A · 50%
Percentage score = \( \frac{20}{40} \times 100 = 50\% \).
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Convert the fraction \( \frac{3}{5} \) into a percentage.
A · 60%
Convert fraction to decimal: \( \frac{3}{5} = 0.6 \). Multiply by 100 gives 60%.
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Convert 0.45 into a percentage.
B · 45%
Multiply 0.45 by 100 to get 45%.
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Which of the following is equal to 25%?
A · 0.25
25% = \( \frac{25}{100} = 0.25 \).
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Express \( \frac{7}{20} \) as a percentage.
A · 35%
\( \frac{7}{20} = 0.35 \), multiplied by 100 gives 35%.
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Find 20% of 150.
A · 30
20% of 150 = \( \frac{20}{100} \times 150 = 30 \).
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Calculate 15% of 200.
A · 30
15% of 200 = \( \frac{15}{100} \times 200 = 30 \).
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A shirt costs $120. What is 12.5% of its cost?
A · $15
12.5% of 120 = \( \frac{12.5}{100} \times 120 = 15 \).
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Find 8% of 375.
A · 30
8% of 375 = \( \frac{8}{100} \times 375 = 30 \).
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If 40 is 25% of a number, what is the number?
A · 160
Let the number be \( x \). Then \( 25\% \times x = 40 \implies x = \frac{40 \times 100}{25} = 160 \).
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If 18 is 30% of a number, find the number.
A · 60
Let the number be \( x \). \( 30\% \times x = 18 \implies x = \frac{18 \times 100}{30} = 60 \).
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40 is 80% of which of the following numbers?
A · 50
Let the number be \( x \). \( 80\% \times x = 40 \implies x = \frac{40 \times 100}{80} = 50 \).
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If 150 is 60% of a number, find the number.
A · 250
Let the number be \( x \). \( 60\% \times x = 150 \implies x = \frac{150 \times 100}{60} = 250 \).
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A price of a product was $200 and increased by 10%. What is the new price?
A · $220
Increase = 10% of 200 = 20, new price = 200 + 20 = $220.
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The value of an item decreased from $150 to $120. What is the percentage decrease?
A · 20%
Decrease = 150 - 120 = 30. Percentage decrease = \( \frac{30}{150} \times 100 = 20\% \) (Correcting: actually 20%). Option A is correct.
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An item's price increased by 25% to reach $250. What was the original price?
A · $200
Let original price be \( x \). \( x + 0.25x = 250 \implies 1.25x = 250 \implies x = 200 \).
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A product originally priced at $400 is discounted by 15%. What is the sale price?
A · $340
Discount = 15% of 400 = 60. Sale price = 400 - 60 = $340.
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If cost price of an article is $150 and it is sold for $180, what is the profit percentage?
A · 20%
Profit = 180 - 150 = 30. Profit % = \( \frac{30}{150} \times 100 = 20\% \).
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A shopkeeper bought an article for $250 and sold it for $225. What is the loss percentage?
A · 10%
Loss = 250 - 225 = 25. Loss % = \( \frac{25}{250} \times 100 = 10\% \).
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If a product was marked 20% above the cost price of $300, what is the marked price?
A · $360
Marked price = 300 + 20% of 300 = 300 + 60 = $360.
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A radio marked at $500 is sold at a discount of 10%. Find the selling price.
A · $450
Discount = 10% of 500 = 50. Selling price = 500 - 50 = $450.
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If a man saves 15% on an article bought for $320, how much money does he save?
A · $48
Saving = 15% of 320 = \( \frac{15}{100} \times 320 = 48 \).
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A man paid $690 for an article after a 10% discount. What was the marked price?
A · $766.67
Selling price = 90% of marked price (M). \( 0.9M = 690 \implies M = \frac{690}{0.9} = 766.67 \).
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A salary increases from $2500 to $2750. What is the percentage increase?
A · 10%
Increase = 2750 - 2500 = 250. Percentage increase = \( \frac{250}{2500} \times 100 = 10\% \).
