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# If r and t are positive integers, is rt even?

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Manager
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If r and t are positive integers, is rt even? [#permalink]  02 Oct 2007, 12:30
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Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 1 sessions
Q28)
If r and t are positive integers, is rt even?

(1) r + t is odd.
(2) r^t is odd.
Director
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Each statement alone is SUFF.

I would chose D.

- Brajesh
Director
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A is sufficient. odd + odd = even. Odd + even = odd. Even + even = even. So if r+t is odd, one of the #'s is odd and one is even. Odd times an even is always even.

B is insufficient. 5^2 is 25, and is odd, and 5*2 is 10, which is even and satisfies the question. But 5^3 is also odd, and 5*3 is 15, which is odd. So you can't tell.

I go with A.
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Manager
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I agree with A.

[1] r+t = odd
The only way we can get an odd integer through addition is to add even+odd = odd. Therefore, we know one is even and one is odd, which is sufficient.

[2] r^t = odd
Knowing the rules of multiplication helps here. The only way to get an odd integer through multiplication is odd*odd = odd. So, the only thing this statement tells us is that r is odd. However, we don't know if t is even or odd. Therefore, this is insufficient.
Director
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uphillclimb wrote:
A is sufficient. odd + odd = even. Odd + even = odd. Even + even = even. So if r+t is odd, one of the #'s is odd and one is even. Odd times an even is always even.

B is insufficient. 5^2 is 25, and is odd, and 5*2 is 10, which is even and satisfies the question. But 5^3 is also odd, and 5*3 is 15, which is odd. So you can't tell.

I go with A.

I am out... Good catch.....
Agree, it's A.

- Brajesh
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Re: GMAT Prep 2: DS Q28 [#permalink]  03 Oct 2007, 10:14
avenger wrote:
Q28)
If r and t are positive integers, is rt even?

(1) r + t is odd.
(2) r^t is odd.

ST. 1
since r+t is odd,
if r=odd & t= even, then rt= even
SUFF

ST. 2
r^t is odd
so if r= odd and t=even then rt= even
but if r=odd and t=odd, then rt= odd
INSUFF

A.
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Re: GMAT Prep 2: DS Q28 [#permalink]  03 Oct 2007, 23:56
avenger wrote:
Q28)
If r and t are positive integers, is rt even?

(1) r + t is odd.
(2) r^t is odd.

Quick and easy A. These are my favorite Quant questions b/c if u know the rules of odds and evens, these probs are a breaze.

rt even?

so either E*E or O*E will give us an even.

S1: r+t = odd. Only E+O yields an odd (when positive integers, r and t are non 0 values and are integers). So this is suff.

S2:
r^t is odd. r^t can be 5^6 or 5^5. Both are still odd, but when multiplied, yield different results.

Insuff.
Manager
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OA is A. I was caught out as well like Brajesh.

Thanks for the explanations.

A.
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