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by rakeshd347 » Thu Oct 17, 2013 8:49 pm
If M and N are integers, is {(10^M)+N}/3 an integer?

(1) N=5

(2) MN is even

I think its clear now.
(10^M)+N/3
Last edited by rakeshd347 on Fri Oct 18, 2013 3:40 pm, edited 1 time in total.
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by theCodeToGMAT » Thu Oct 17, 2013 8:54 pm
Is the question

[10^(M+N)]/3

Or,

((10^M)+N)/3
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by Brent@GMATPrepNow » Fri Oct 18, 2013 10:29 am
I have a feeling that the question should read is (10^M + N)/3 an integer?
I also have a feeling that the original question probably restricts M and N to positive integers.

However, if we go with the wording below . . .
If M and N are integers, is (10^M + N)/3 an integer?
1) N = 5
2) MN is even
. . . then the answer is E

Here's why.

Target question: Is (10^M + N)/3 an integer?

Statements 1 and 2 combined
There are several values of M and N that satisfy BOTH statements. Here are two:
Case a: M = 2 and N = 5. Here, (10^M + N)/3 = 105/3 = 35. So, (10^M + N)/3 is an integer
Case b: M = -2 and N = 5. Here, (10^M + N)/3 = 5.01/3 = 1.67. So, (10^M + N)/3 is not an integer
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

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Brent
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by [email protected] » Sat Oct 19, 2013 12:11 pm
Hi rakeshd347,

Brent brings up an interesting point; the "intent" of the question is PROBABLY to restrict you to POSITIVE INTEGERS for M and N. GMAT questions are always worded with the necessary attention to detail, so you have to follow whatever "instructions" you're given.

**IF this question included the restriction that M and N were POSITIVE integers, then here's what the solution would be:**

Is (10^M + N)/3 an integer. This is a Yes/No question.

Fact 1: N = 5
There's actually an interesting Number Property here....
The M can be any positive integer, so we'll end up with 10 or 100 or 1000 or 10000, etc.
When you add 5 to any of those numbers, you end up with a number that is divisible by 3:
15 = 5 x 3 and the answer is YES.
105 = 35 x 3 and the answer is YES.
1005 = 335 x 3 and the answer is YES.
etc.
Fact 1 is SUFFICIENT.

Fact 2: MN = even
If M = 2, N = 1 then we have 101 and the answer is NO
If M = 2, N = 5 then we have 105 and the answer is YES
Fact 2 is INSUFFICIENT.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
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