If an 11 digit number 5y5884805x6 is divisible by 72 then the value of is ........

Quantitative Aptitude (CGL) Number System

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If an 11-digit number 5y5884805x6, is divisible by 72, then the value of $\sqrt{xy}$ is:

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SSC CGL 10 June 2019 Shift-1

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$\sqrt{7}$

$2\sqrt{7}$

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Explanation:

5y5884805x6 will be divisible by 72
to divide that no it should be divided by 9 and 8 both
1. for divisibility by 8 the last three digit will be divided by 8 the last three digits are 5x6 so x will be 7
2. for divisibility by 9 the sum of all digits will be divisible by 9
3. Sum of all digits = 5+y+5+8+8+4+8+0+5+7+6=56+y, so y will be 7
4. $\sqrt{xy}$ = $\sqrt{7\times 7}$ =7