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SSC CGL 2022 PYQ — Question 73

SSC CGL Tier II - Quant - 29 Jan 2022 • Quantitative Aptitude • Q73

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If a 10-digit number 75462A97B6 is divisible by 72, then the value of 8A−4B\sqrt{8A-4B}is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. √28

75462A97B6 is divisible by 2

Co - prime factors of 72 = 9 and 8.

75462A97B6 is divisible by 8, which means 7B6 is divisible by 8.

The possible value of b at which 7B6 is divisible by 8 is 3 and 7.

If 75462A97B6 is divisible by 9 then the sum of the digits of 75462A97B6 is also divisible by 9

7 + 5 + 4 + 6 + 2 + A + 9 + 7 + B + 6 = 45 + 1 + A + B.

A + B + 1 must be divisible by 9,

At B = 3 possible value of A is 5

At B = 7 No value of A is possible.

8A−4B\sqrt{8A-4B} = 40−12=28\sqrt{40 - 12} = \sqrt{28}.