Aptitude - Number System Online Test, Number System Questions and Answers updated

Solution: Sqrt(551) > 22
All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23.
119 is divisible by 7; 187 is divisible by 11;
247 is divisible by 13 and 551 is divisible by 19.
So, none of the given numbers is prime.

Solution: Let the two consecutive even integers be 2n and (2n + 2).
Then the difference of squares of these two consecutive even integers = (2n + 2)^2 – (2n)^2
= (2n)^2 + 8n + 4 – (2n)^2
= 8n + 4
= 4(2n + 1)
=> which is divisible by 4

Solution: Let x = 6q + 3. Then, x^2 = (6q + 3)^2 = 36q2 + 36q + 9 = 6(6q2 + 6q + 1) + 3 Thus,
when x2 is divided by 6, then remainder = 3.

Solution: 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 number is 202860.

Solution: For every natural number n, (x^n - a^n) is completely divisible by (x - a).

Solution: 35423 317 x 89 = 317 x (90 -1 ) + 7164 = (317 x 90 - 317) + 41720 = (28530 - 317) ----- = 28213 84307 - 28213 ----- 56094 -----

Solution: Given Exp. = (397)^2 + (104)^2 + 2 x 397 x 104 = (397 + 104)^2 = (501)2 = (500 + 1)^2 = (500^2) + (1)^2 + (2 x 500 x 1) = 250000 + 1 + 1000 = 251001

Solution: Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2. Thus, when 2n is divided by 4, the remainder is 2.

Solution: Let 4300731 - x = 2535618 Then x, = 4300731 - 2535618 = 1765113

Solution: On dividing we get,
88) 9217 (104 88 ---- 417 352 ---- 65 ---- Therefore,
Required number = 9217 + (88 - 65) // Because (88 - 65) < 65. = 9217 + 23 = 9240.

Solution: Given
639 is not divisible by 7
2079 is divisible by each of 3, 7, 9, 11.
So, 2079 is a correct answer.

Solution: 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 is, x = 6.
Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9. Required value of * is 6.

Solution: On dividing, we get
75) 8485 (113 75 --- 98 75 ---- 235 225 --- 10 --- Required number = (8485 - 10) // Because 10 < (75 - 10) = 8475.

Solution: (800 ÷ 64) x (1296 ÷36) = 12.5 * 36 = 450

Solution: Prime numbers less than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 Their number is 15

Solution: 987 = 3 x 7 x 47 So, the required number must be divisible by each one of 3, 7, 47
553681 (Sum of digits = 28, not divisible by 3)
555181 (Sum of digits = 25, not divisible by 3)
555681 is divisible by 3, 7, 47.

Solution: Clearly, (2272 - 875) = 1397, is exactly divisible by N. Now, 1397 = 11 x 127 The required 3-digit number is 127, the sum of whose digits is 10.

Solution: 6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x. Then, (5 + x + 2) must be divisible by 3. So, x = 2.

Solution: Given number = 97215x6 (6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11. x = 3

Solution: Let the given number be 476 xy 0. Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3. And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.
x - y - 3 = 0 y = x - 3 (17 + x + y) = (17 + x + x - 3) = (2x + 14) x= 2 or x = 8. Therefore, x = 8 and y = 5.