Divisibility Test
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Practice questions:

X = 1234…….616263. What will be the remainder if x is divided by 8 and 9 and 72?

In above question if you add all digits till you get a single digit, what that digit will be?

The sixdigit number 73A998 is divisible by 6, How many values of A are possible?

A hundred digit number is for med by writing first 54 natural numbers one after the other as 123456…………….5354. Find the remainder when this number is divided by 8.

If 233 is divided by a certain number n it gives remainder 5. What will be the remainder 466 is divided by 2n assuming the quotient is same in both the cases.

For which of the following values of n is (100 + n)/n NOT an integer ?
(A) 1 (B) 2 (C) 3 (D) 4
(E) 5

If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6 ?
(A) 0 (B) 1 (C) 2 (D) 3
(E) 4

If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M + N?
(A) 86 (B) 52 (C) 34 (D) 28
(E) 10

When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?
(A) 23x + 17y = 19 (B) 17x – 23y = 9
(C) 17x + 23y = 19 (D) 14x + 5y = 6
(E) 5x – 14y = –6

If when 950 and 1170 are divided by a natural number d, the remainders obtained are 18 and 5 respectively, then d is a t most
(A) 117 (B) 247 (C) 223 (D) 123

pq, qr, qp and pp are twodigit numers, 'pqr' is a threedigit number and 'prrp' is a fourdigit number (p, q, r are all numerals.) If pq x pr = pqr, then the remainder when (qp x prrp) is divided by 'pp' is
(A) 0 (B) 1
(C) 7 (D) None of these

Given that a, b, c and d are positive integers such that b^{3/2} = a, and d^{5/4} = c. If b – d = 9. then find the value of (a – c).
(A) 92 (B) 94 (C) 95 (D) 93

For how many values of n less than 17, n being a positive integer, is n! + (n + 1)! (n + 2)! an integral multiple of 49 ?
(A) 5 (B) 2 (C) 3 (D) 1