Number System MCQs

P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q = ?

How many numbers less than 1000 are multiple of both 10 and 13 ?

If (1012 + 25)2 - (1012 - 25)2 = 10n, then the value of n is :

Which of the following numbers is divisible by 3, 7, 9 and 11 ?

When a certain positive integer P is divided by another positive integer, the remainder is $${r_{1}}$$ . When a second positive integer Q is divided by the same integer, the remainder is $${r_{2}}$$ and when (P + Q) is divided by the same divisor, the remainder is $${r_{3}}$$ . Then the divisor may be :

For the integer n, if n3 is odd, then which of the following statements are true ? I. n is odd II. n2 is odd III. n2 is even

A 9 digit number in which zero does not appear and no digits are repeated has the following properties: The number comprising the left most two digits is divisible by 2, that comprising the left most three digits is divisible by 3, and so on

The remainder obtained when any prime number greater than 6 is divided by 6 must be :

The smallest number which must be subtracted from 8112 to make it exactly divisible by 99 is :