The number N is 5H72, the hundred's digit being represented by H. What

Question

The number N is 5H72, the hundred's digit being represented by H. What is the value of H?

(1) N is divisible by 4.
(2) N is divisible by 9.

doomedcat · Answer

1) not suff as /4 last two digit must be /4, nothing for H
2) Since it is divisible by 9, sum if the digits must be divisible by 9 , so we have 14+H should be divisible by 9, now H can have only 4 as values so as to be 18, hence H=4 suff

Sprincejindal · Answer

Is the Statement I correct? How can N be divisible by 4 if the sum of last two digits is not divisible by 4? 
I know even if the sum of last two digits was divisible by 4 the answer will still be insufficient. But I am not sure if the statement I is correct.

Bunuel · Answer

An integer to be divisible by 4, the last two digits must be divisible by 4, not the sum of the last two digits. For example, 1233 56  is divisible by 4 because  56  is divisible by 4.

amanvermagmat · Answer

(1) For a number to be divisible by 4, its last two digits must be divisible by 4. So in case of 5H72, since last two digits are divisible by 4 (72 is a multiple of 4), 5H72 WILL be divisible by 4, irrespective of the value of H (meaning H can take any value from 0 to 9 doesnt matter). So Insufficient.

(2) For a number to be divisible by 9, its sum of digits must be divisible by 9. So 5+H+7+2 = 14+H must be divisible by 9. We can see that H can thus take only one value of '4', which will make sum of digits as 18, and thus divisible by 9. Sufficient.

Hence  B answer

ccooley · Answer

Here's an interesting variant of this problem that I thought of while solving this one! In this case, the answer is E, even though all I did was change the number slightly...

Bunuel · Answer

Thank you. Posted it  HERE .

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The number N is 5H72, the hundred's digit being represented by H. What

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GMAT Data Sufficiency (DS) Questions

The number N is 5H72, the hundred's digit being represented by H. What

Prep Toolkit

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