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Intern  Joined: 18 Jun 2012
Posts: 21
GMAT Date: 09-17-2012
Is the tens digit of a two digit integer k divisible by 3?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 69% (02:30) correct 31% (02:08) wrong based on 219 sessions

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Is the tens digit of a two digit integer k divisible by 3?

(1) k-5 is a multiple of 3
(2) k-11 is a multiple of 3

Originally posted by ananthpatri on 05 Aug 2012, 23:12.
Last edited by Bunuel on 06 Aug 2012, 00:21, edited 1 time in total.
Intern  Joined: 08 Apr 2012
Posts: 4
Location: India
GMAT Date: 08-25-2012
WE: Law (Law)
Re: Is the tens digit of a two digit integer k divisible by 3?  [#permalink]

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The Answer is E.

For the first statement, select k as 44. k-5=39 which is divisible by 3, the tens digit is 4 which is not divisible by 3. Then select k as 38. k-5=33 which is divisible by 3 and tens digit of 38 is divisible by 3. As both yes and no possible, insufficient.

Similarly, for statement 2 both yes and no are possible.

If we take 1 and 2 together still both outcomes are possible.

Hence, answer is E.
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Is the tens digit of a two digit integer k divisible by 3?  [#permalink]

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Is the tens digit of a two digit integer k divisible by 3?

(1) k-5 is a multiple of 3 --> $$k-5=3m$$ --> $$k=3m+5=3(m+1)+2$$. So, we have that $$k$$ is 2 more than a multiple of 3. Now, if $$k=11$$ (2 more than 9), then the answer is NO, but if $$k=32$$ (2 more than 30), then the answer is YES. Not sufficient.

(2) k-11 is a multiple of 3 --> $$k-11=3n$$ --> $$k=3n+11=3(n+3)+2$$. The same info as above: $$k$$ is 2 more than a multiple of 3. Not sufficient.

(1)+(2) Nothing new. Not sufficient.

P.S. Please provide OA's for the questions you post. Rule #7 here: rules-for-posting-please-read-this-before-posting-133935.html If you don't have OA you must indicate that in the post.
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Intern  Joined: 18 Jun 2012
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Re: Is the tens digit of a two digit integer k divisible by 3?  [#permalink]

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Thanks for the answer.
SVP  Joined: 06 Sep 2013
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Concentration: Finance
Re: Is the tens digit of a two digit integer k divisible by 3?  [#permalink]

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We need to know if the tens digit of two digit integer K is divisible by 3, that is also to know whether a can be 3,6 or 9. Statement 1 tells us that k =3p+5, we can find statements satisfying both scenarios (E.g. k=35 yes or k=80 no).

Second statement, k = 3p+11. Same here.

Both together we still can find both scenarios either tens digit is divisible by 3 or not.

E is the correct answer
Hope this clarifies
Cheers!
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Re: Is the tens digit of a two digit integer k divisible by 3?  [#permalink]

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Bunuel wrote:
Is the tens digit of a two digit integer k divisible by 3?

(1) k-5 is a multiple of 3 --> $$k-5=3m$$ --> $$k=3m+5=3(m+1)+2$$. So, we have that $$k$$ is 2 more than a multiple of 3. Now, if $$k=11$$ (2 more than 9), then the answer is NO, but if $$k=32$$ (2 more than 30), then the answer is YES. Not sufficient.

(2) k-11 is a multiple of 3 --> $$k-11=3n$$ --> $$k=3n+11=3(n+3)+2$$. The same info as above: $$k$$ is 2 more than a multiple of 3. Not sufficient.

(1)+(2) Nothing new. Not sufficient.

P.S. Please provide OA's for the questions you post. Rule #7 here: rules-for-posting-please-read-this-before-posting-133935.html If you don't have OA you must indicate that in the post.

Hi, Bunuel

If I understood correctly both functions leave remainder of 2 and that'swhy you understood that combination wouldn't add anything new.
(by the way in your explanation you named 3m+5 and the other 3n+11, why don't we name them both n or m, is it because when we name it that way we get equation like 0=6 ?)
But what if 2nd statement was k+10 or k+7 , which would be K=3*(m+1)+1 and , how would you solve that one and know combination of both statements wouldn't provide answer.

B) on the GMAT how you can determine whether it is better to use function as you always do or put number. Of course you provide detailed answer , but I think here it could be more efficient to use number. Want to know your opinion

Thank You
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Re: Is the tens digit of a two digit integer k divisible by 3?  [#permalink]

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_________________ Re: Is the tens digit of a two digit integer k divisible by 3?   [#permalink] 24 Jan 2018, 23:28
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