m p t

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

m p t

by sanju09 » Wed Mar 09, 2011 4:23 am

If m, p, and t are positive integers and m < p < t, is the product m p t an even integer?

I. t - p = p - m.

II. t - m = 16.

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Source: Beat The GMAT — Data Sufficiency | Wed Mar 09, 2011 4:23 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Mar 09, 2011 5:03 am

The product mpt will be even if any of m, p, or t is even.
(1) t - p = p - m implies 2p = t + m
Let m = 3, p = 4, t = 5. Here m < p < t and t + m = 2p.
Also, mpt is even.
Next let m = 5, p = 7, t = 9. Here m < p < t and t + m = 2p.
But mpt is odd.
No unique answer.
So, (1) is NOT SUFFICIENT.

(2) t - m = 16.
Let m = 9, p = 11, t = 25. Here m < p < t, t - m = 16.
Also, mpt is odd.
Next, let m = 9, p = 10, t = 25. Here m < p < t. t - m = 16.
But, mpt is even.
No unique answer.
So, (2) is NOT SUFFICIENT.

Combining (1) and (2), if m = 1, p =9, t = 17. Here m < p < t, t - m = 16 and t + m = 2p.
Here mpt is odd.
Next let m = 2, p = 10, t = 18. Here m < p <t, t-m = 16 and t+m = 2p.
But mpt is even.
Again no unique answer.

The correct answer is E.

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