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Question

710 − 510  is divisible by

This question was previously asked in
CDS I 2016 English Previous Year Paper (14-Feb-2016)
The correct answer is

11

Applied Concept:

(a2 − b2 ) = (a + b) (a − b)

Divisibility Rule of 11: If the difference between the sum of alternate digits of a number is divisible by 11, then the number is completely divisible by 11.

Calculation:

It is given that,

710 − 510

⇒ (75 + 55) (75 − 55)    

⇒ 75 = 343 × 49 = 16807

⇒ 55 = 625 × 5 = 3125

⇒ 710  − 510 = 19932(75 − 55)

Now, for the number 19932 ,

Sum of odd-positioned digits = 2 + 9 + 1 = 12

Sum of even-positioned digits = 9 + 3 = 12

Therefore, the difference = 12 − 12 = 0

∴ The number is divisible by 11.

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    select the correct answer using the code given below:

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