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

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

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New post 12 Dec 2017, 05:50
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Re: The number N is 5H72, the hundred's digit being represented by H. What  [#permalink]

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New post 12 Dec 2017, 09:17
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
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Re: The number N is 5H72, the hundred's digit being represented by H. What  [#permalink]

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New post 13 Dec 2017, 06:56
Bunuel wrote:
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.


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.
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Re: The number N is 5H72, the hundred's digit being represented by H. What  [#permalink]

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New post 13 Dec 2017, 07:01
Sprincejindal wrote:
Bunuel wrote:
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.


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.


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, 123356 is divisible by 4 because 56 is divisible by 4.
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Re: The number N is 5H72, the hundred's digit being represented by H. What  [#permalink]

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New post 13 Dec 2017, 10:52
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Bunuel wrote:
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.


(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
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Re: The number N is 5H72, the hundred's digit being represented by H. What  [#permalink]

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New post 13 Dec 2017, 14:37
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Here's an interesting variant of this problem that I thought of while solving this one!

Quote:
The number N is 6H12, 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.


In this case, the answer is E, even though all I did was change the number slightly... :)
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Re: The number N is 5H72, the hundred's digit being represented by H. What  [#permalink]

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New post 13 Dec 2017, 20:27
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Re: The number N is 5H72, the hundred's digit being represented by H. What   [#permalink] 13 Dec 2017, 20:27
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