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CDS | Elementary Mathematics | Divisibility Rule

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Question 1

What is the sum of the digits of the least number which, when divided by 52, leaves 33 as remainder; when divided by 78, leaves 59 and when divided by 117, leaves 98 as remainder ?

Question 2

Consider the following assumption and two statements :
Assumption : A number ‘ABCDE’ is divisible by 11.
Statement-I : E – D + C – B + A is divisible by 11.
Statement- II : E - D + C – B + A =0.
Which one of the following is correct ?

Question 3

On dividing a certain number by 342, we get 47 as remainder. If the same number id divided by 18, what will be the remainder?

Question 4

A five-digit number XY235 is divisible by 3 where X and Y are digits satisfying What is the number of possible pairs of values of (X, Y)?

Question 5

Consider the following statements in respect of three 3-digit numbers XYZ, YZX and ZXY:
1) The sum of the numbers is not divisible by
2) The sum of the numbers is divisible by 111.
Which of the above statements is/are correct?
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Mar 27CDS & Defence