All Free Mathematics MCQs with Answers

• A. 3
• B. 11
• C. 13
• D. None of these

Explanation: The sum is 461 + 462 + 463 + 464 = 1850. It is not divisible by 3 because its digit sum is 14, not by 11 because 11 x 168 = 1848, and not…

• A. 100
• B. 300
• C. 90,000
• D. 10,000Fun & Trivia

Explanation: Evaluate the division from left to right: 84 ÷ 14 ÷ 2 ÷ 9 = 6 ÷ 2 ÷ 9 = 3 ÷ 9 = 1/3. Therefore (1/3) × ? = 33 1/3 = 100/3, so ?

• A. 480m
• B. 320m
• C. 400m
• D. 450m

Explanation: Let the length and breadth be 3k metres and 2k metres. Their difference is k metres, and it is given as 40 metres, so k = 40 metres; the…

• A. 50%
• B. 60%
• C. 40%
• D. 64%

Explanation: Areas of circles are proportional to the squares of their radii, so the area ratio is 3²:5² = 9:25.

• A. 1:3
• B. 1:6
• C. 1:9
• D. 1:5

Explanation: Circle area varies as the square of radius. Squaring the radius ratio 1:3 gives areas 1²:3² = 1:9.

• A. 101
• B. 103
• C. 107
• D. 113

Explanation: If two numbers leave the same remainder, their difference must be exactly divisible by the required divisor.

• A. 17
• B. 29
• C. 23
• D. 31

Explanation: 7429 = 17 x 19 x 23, so these are the first three primes. Since 12673 = 19 x 23 x 29, the fourth prime is 12673 ÷ (19 x 23) = 29.

• A. 50
• B. 36
• C. 24
• D. 12

Explanation: The largest equal box capacity is the HCF of the three quantities because each quantity must be divided into whole boxes without mixing.

• A. 51
• B. 61
• C. 47
• D. 45

Explanation: To minimise the number of equal casks, use the greatest common capacity: HCF(435 L, 493 L, 551 L) = 29 L.

• A. 53
• B. 112
• C. 108
• D. 106

Explanation: If the remainders are equal, the greatest divisor must divide the differences between the numbers.

• A. 12
• B. 18
• C. 24
• D. 32Everyday Science Quiz

Explanation: A divisor giving the same remainder to all three numbers must divide their pairwise differences.

• A. 700,400
• B. 820,360
• C. 800,500
• D. 820,369

Explanation: Work backwards through the Euclidean algorithm with final divisor 41. The pair 820 and 369 gives 820 = 2 x 369 + 82, 369 = 4 x 82 + 41…

• A. 3600
• B. 504
• C. 441
• D. 7056

Explanation: The LCM of 21, 36 and 56 is 2^3 x 3^2 x 7 = 504. To make this a perfect square, the odd power of 2 must be supplied by another factor of…

• A. 36
• B. 66
• C. 132
• D. 264

Explanation: For two numbers, product = HCF x LCM. Thus the product is 12 x 396 = 4752, and the other number is 4752 ÷ 36 = 132.

• A. 1080
• B. 10080
• C. 10025
• D. 11080

Explanation: The LCM of 12, 15 and 18 is 180. The first five-digit multiple is 180 x 56 = 10080, because 180 x 55 = 9900 is still four digits.

• A. 31
• B. 41
• C. 51
• D. 61

Explanation: The number must leave remainder 1 when divided by 2, 3 and 5, so it is 1 more than a multiple of LCM(2, 3, 5) = 30.

• A. 1439
• B. 1440
• C. 1459
• D. 1449Pakistan Studies Quiz

Explanation: If the number increased by 1 is divisible by all the given numbers, first find their LCM: LCM(12, 18, 24, 32, 40) = 1440.

• A. 10085
• B. 10080
• C. 10075
• D. 10070

Explanation: The least five-digit multiple of 144 is found by taking the first multiple at or above 10000: 144 x 69 = 9936, while 144 x 70 = 10080.

• A. 9930
• B. 9903
• C. 9935
• D. 9936

Explanation: The greatest four-digit multiple of 144 is obtained from 144 x 69 = 9936; the next multiple, 144 x 70 = 10080, has five digits.

• A. 1080
• B. 1085
• C. 1075
• D. 1095

Explanation: The least common multiple of 4, 6, 8 and 10 is 120, since 120 is the smallest number divisible by all four.