Numbers

Question: If the number 42573 * is exactly divisible by 72, then the minimum value of * is: [A]. 4 [B]. 5 [C]. 6 [D]. 7 Answer: Option C Explanation: 72 = 9 x8, where 9 and 8 are co-prime. The minimum value of x for which 73x for which 73x is divisible by 8…

Question: Which one of the following numbers is completely divisible by 99? [A]. 3572404 [B]. 135792 [C]. 913464 [D]. 114345 Answer: Option D Explanation: 99 = 11 x 9, where 11 and 9 are co-prime. By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by…

Question: Which one of the following numbers is completely divisible by 45? [A]. 181560 [B]. 331145 [C]. 202860 [D]. 2033555 Answer: Option C Explanation: 45 = 5 x 9, where 5 and 9 are co-primes. Unit digit must be 0 or 5 and sum of digits must be divisible by 9. Among given numbers, such…

Question: If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be: [A]. 1 [B]. 2 [C]. 3 [D]. 4 Answer: Option C Explanation: Then number 6×2 must be divisible by 8.    x = 3, as 632 is divisible 8.

Question: If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be: [A]. 3 [B]. 2 [C]. 1 [D]. 5 Answer: Option A Explanation: Given number = 97215×6 (6 + 5 + 2 + 9) – (x + 1 + 7) = (14 –…

Question: If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be: [A]. 2 [B]. 5 [C]. 6 [D]. 7 Answer: Option D Explanation: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 +…

Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be: [A]. 0  [B]. 1 [C]. 2 [D]. None of these Answer: Option C Explanation: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22…

Question: What is the unit digit in 7105 ? [A]. 1 [B]. 5 [C]. 7 [D]. 9 Answer: Option C Explanation: Unit digit in 7105 = Unit digit in [ (74)26 x 7 ] But, unit digit in (74)26 = 1 Unit digit in 7105 = (1 x 7) = 7

Question: If (64)2 – (36)2 = 20 x x, then x = ? [A]. 70 [B]. 120 [C]. 180 [D]. 140 Answer: Option D Explanation: 20 x x = (64 + 36)(64 – 36) = 100 x 28      x = 100 x 28 = 140 20

Question: 397 x 397 + 104 x 104 + 2 x 397 x 104 = ? [A]. 250001 [B]. 251001 [C]. 260101 [D]. 261001 Answer: Option B Explanation: Given Exp. = (397)2 + (104)2 + 2 x 397 x 104 = (397 + 104)2 = (501)2 = (500 + 1)2 = (5002) + (1)2 +…