Which statement is true

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Xeb: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Mon Jan 04, 2010 10:38 am; Thanked: 2 times

by Xeb » Mon Oct 03, 2011 4:18 am

If n and k are integers whose product is 400, which of the following statements must be true?

(A) n + k > 0
(B) n â‰ k
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E)If n is odd, then k is even.

My test prep book shows me the answer is (E), but isn't that the same as (D)? I would choose (C).

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Oct 03, 2011 4:31 am

Theres a difference.

If the first number is chosen to be even, it doesnt matter what the second number is, the product will be even.

But if the first is chosen to be odd, it is absolutely necessary that the second number be even for the product to be even.

Hence E is absolutely essential whereas D may or may not be

Also C need not be true for you could have cases like 25*16 = 400 but neither 25 nor 16 are multiples of 10

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Mon Oct 03, 2011 10:11 am

Wanted to add a quick comment about choice C:

Choice C can be translated as:
Either n or k contains both 2 and 5 in its prime factorization.
If you think of it this way, you can quickly conclude that there is no reason why all the 2's can't be in one number and all of the 5's in the other number. You don't really need to think about what the actual numbers themselves (16, 25) are.

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rohit_gmat: Master | Next Rank: 500 Posts; Posts: 158; Joined: Wed Jun 16, 2010 8:21 amFollowed by: 1 member; Thanked: 13 times

by rohit_gmat » Mon Oct 03, 2011 9:13 pm

Xeb wrote:If n and k are integers whose product is 400, which of the following statements must be true?

(A) n + k > 0
(B) n â‰ k
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E)If n is odd, then k is even.

My test prep book shows me the answer is (E), but isn't that the same as (D)? I would choose (C).

the gmat often does that (create 2 answer choices that look like they are the same) in such Qs... and when we see that one is false, we incorrectly assume that the other must also be false too... but thats not always the case..
the best way to do this (according to me) is to plug in numbers that contradict the statement..

A) n + k > 0 .......(-20 x -20 = 400) -20 + -20 = -40 (>0? .. NO)
B) n != k ....... can use above example .. NO
C) (i left this initially coz it didnt look so easy to find a contradiction.. so i thot maybe this is the correct answer)
D) n even, then k is odd .... can use example in A&B ... n is even & so is k
E) (cant find anything)

So i went back to C

C) I tried to seperate the 5s from the 2s (to prevent a 10) and got : 25 x 8 ... NO

answer is E

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

by Anurag@Gurome » Mon Oct 03, 2011 9:14 pm

Xeb wrote:If n and k are integers whose product is 400, which of the following statements must be true?

(A) n + k > 0
(B) n â‰ k
(C) Either n or k is a multiple of 10.
(D) If n is even, then k is odd.
(E)If n is odd, then k is even.

My test prep book shows me the answer is (E), but isn't that the same as (D)? I would choose (C).

A. n = k = -20 --> (n +k) = -40 < 0 ----> FALSE
B. n = k = 20 ---------------------------> FALSE
C. n = 16 and k = 25 --------------------> FALSE
D. n = 2 and k = 400 --------------------> FALSE
E. If n is odd then k must be even as their product is even ---> TRUE

The correct answer is E.

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