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

Question

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

sah130 · Answer

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.

Bunuel · Answer

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.

Answer: E.

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.

ananthpatri · Answer

Thanks for the answer.

jlgdr · Answer

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!
J

Resad95 · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards