Dear Reader, Below are three simple numeric questions dealing with divisibility of numbers.

Question 1

Rama and Krishna posed riddles to each other. Rama asked Krishna :” If x and y are the two digits of the number 179xy such that this number is divisible by 70, then x + y is equal to:”

a) 2 b) 8 c) 3 d) 6

Answer : a) 2

Solution :

Since the number is divisible by 70 the last digit i.e y should be 0.
Options given represent sum of x and y. As we have found out y = 0, sum of x and y should be x. Therefore the options represent the x digit. Based on the options given, the number has to 17920 or 17980 or 17930 or 17960. Of these 17920 alone is divisible by 70 without remainder. So 2 + 0 = 2.

Question 2

Draupadhi and Seethadevi met in a restaurant after a gap of many years. Seethadevi posed a problem which has been in her mind for quite some tome to Draupadhi. The problem read as under:
“ If the number 2735X is divisible by 11 , what is the value of X?

a) 6 b) 7 c) 8 d) 9

Answer : b) 7

Solution :

Rule for divisibility by 11—
1. Add the odd-numbered digits together (the first, third, fifth, etc). 
2. Add the even-numbered digits together (the second, fourth, sixth, etc). 
3. Subtract the smaller number from the bigger number. If the number you get is divisible by 11, then so is the original number. (0 is divisible by 11).

Following the above rule,
(2 + 3 + X) – (7+5) , if it is zero or divisible by 11 then the number is divisible by11.
Applying the choices, choice b)-7 -- gives 12 – 12 = 0 and that is the answer. Other choices do not fit in.

Question 3

Two friends were preparing for competitive examinations and they came across a problem which reads as under:
“ If x and y are the two digits of the number 140x4y such that this number is divisible by 60, then x + y is equal to:”

a) 2 b) 4 c) 1 d) 6

Answer : d) 6

Solution :

For the number to be divisible by 60, the unit digit i.e y has to be 0.

Since options are sums of x and y, with y being 0, each of them represent x.

Therefore, as per the options, the number has to be 140240 or 140440 or 140140 or 140640

Among these, only 140640 is perfectly divisible by 60. Hence answer is option d) 6.