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If n and k are integers whose product is 400, which of the following

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If n and k are integers whose product is 400, which of the following  [#permalink]

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New post Updated on: 03 Aug 2018, 10:10
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A
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D
E

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

A. n+k>0
B. n does not equal 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

D and E sound the same to me. Please help explain.

Originally posted by chintzzz on 19 Jun 2010, 21:34.
Last edited by Bunuel on 03 Aug 2018, 10:10, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If n and k are integers whose product is 400, which of the following  [#permalink]

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New post 20 Jun 2010, 06:46
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chintzzz wrote:
If n and k are integers whose product is 400, whcih of the following statements must be true?
A.n+k>0
B.n does not equal 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

D and E sound the same to me. Please help explain.


Note that the question is: "whcih of the following must be true?"

Given: \(nk=400\)

For the product of two integers to be even at least one integer must be even.

D says: If n is even, then k is odd --> not necessarily true, n can be even and k be even too --> \(nk=20*20=400\);
E says: If n is odd, then k is even --> this must be true, if one of the factors is odd (n) the second one (k) must be even for their product to be even.

Other choices:

A. n+k>0 --> not necessarily true: \(nk=(-20)*(-20)=400\);
B. n does not equal k --> not necessarily true: \(nk=20*20=400\);
C. Either n or k is a multiple of 10 --> not necessarily true: \(nk=16*25=400\).

Answer: E.

Hope it's clear.
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Re: If n and k are integers whose product is 400, which of the following  [#permalink]

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New post 19 Jun 2010, 22:03
in the question they are saying statements so more than 1 can be correct so both answers D and E are correct.

what are the answer choices ?
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Re: If n and k are integers whose product is 400, which of the following  [#permalink]

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New post 24 Dec 2015, 12:11
chintzzz 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 does not equal 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

D and E sound the same to me. Please help explain.

Make prime factorization of 400. 400=(5^2)*(2^4) or 25*16
A. May be true. What if n=-25 and k=-16? Out
B. May be true. 400=(20^2) hence n=k
C. Not necessarily. n=25 and k=16
D.Not necessarily. n=20 and k=20
E. n=25 and k=16 or n=5 and k=80 Correct
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Re: If n and k are integers whose product is 400, which of the following  [#permalink]

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New post 03 Aug 2018, 10:07
chintzzz 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 does not equal 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

D and E sound the same to me. Please help explain.


Bunuel tell me that my solution is correct now :)

A. n+k>0 ( -20)+(-20) = -40 INCORRECT
B. n does not equal k ( 20 *20 )= 400 INCORRECT
C. Either n or k is a multiple of 10 (25 *16 ) = 400 INCORRECT
D. If n is even, then k is odd (2 *200 = 400) INCORRECT
E. If n is odd, then k is even ( 25*16 = 400) CORRECT
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Re: If n and k are integers whose product is 400, which of the following  [#permalink]

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New post 08 Feb 2020, 20:27
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Re: If n and k are integers whose product is 400, which of the following   [#permalink] 08 Feb 2020, 20:27
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