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Manager  Joined: 16 Feb 2012
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Concentration: Finance, Economics
If n and k are integers whose product is 400, which of the  [#permalink]

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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 is not equal to 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.

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

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

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.

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: $$nk=16*25=400$$.
D. 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. 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.

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

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Ohh..this one was really fun..got screwed up btw D and E. Didn't read between the lines. Thanks for explaining Bunuel.
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Re: If n and k are integers whose product is 400, which of the  [#permalink]

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

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.

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: $$nk=16*25=400$$.
D. 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. 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.

Hope it's clear.

I need just to know that if n is odd, k is even. this is enough to tick e. no need explanation more.
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Re: If n and k are integers whose product is 400, which of the  [#permalink]

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

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.

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: $$nk=16*25=400$$.
D. 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. 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.

Hope it's clear.

in the test room, we can not find 25x16=400 easily. so, if we see E, if n is odd then k is even

tick choice E. that is done.
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Re: If n and k are integers whose product is 400, which of the  [#permalink]

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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 n and k should have the same sign, but that means that they can also both be negative
B.n is not equal to k. 20 x 20 = 400[i]
C. Either n or k is a multiple of 10. [i]25 x 16 = 400

D. If n is even, then k is odd. k can also be even since even x even will be even
E. If n is odd, then k is even. k must be even since odd x even = even
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Re: If n and k are integers whose product is 400, which of the  [#permalink]

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Stiv 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 is not equal to 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.

Since an even product must contain at least 1 even number in the multiplication, if n is odd, then k must be even.

If you had difficulty differentiating between choices D and E, consider the wording. Choice D states that if we are given that n is even, then k must be odd, which is not necessarily true, because k could be even. Take n = 20 and k = 20 for instance (which also eliminates answer choice B). However, Choice E states that if we are given that n is odd, then k must be even. This is a true statement, because the product nk is even.

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Director  P
Joined: 29 Jun 2017
Posts: 933
Re: If n and k are integers whose product is 400, which of the  [#permalink]

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we should begin with 400=2^2*5^2*2^2

from this we see that all condition except choice E can be correct but must not be correct.
Manager  B
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Re: If n and k are integers whose product is 400, which of the  [#permalink]

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Aki wrote:
Ohh..this one was really fun..got screwed up btw D and E. Didn't read between the lines. Thanks for explaining Bunuel.

Same here. I read D and E as: If one is even, the other is odd.

By this logic, I found D and E to be exactly the same Senior Manager  S
Joined: 12 Sep 2017
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If n and k are integers whose product is 400, which of the  [#permalink]

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Hello JeffTargetTestPrep Bunuel

Which is the difference between statements D and E?

Both of them are saying that if one is even, then the second integer should be odd.

D. If n is even, then k is odd.
E. If n is odd, then k is even.

(N even)(K odd) = Even When N = 16, K = 25

(K even)(N odd) = Even When K = 16, N = 25
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Re: If n and k are integers whose product is 400, which of the  [#permalink]

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Stiv 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 is not equal to 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.

Let’s go through the choices.

Since n can be -20 and k can be -20, we see that choice A is not true.

Since n can be 20 and k can be 20, we see that choice B is not true.

Since 400 = 16 x 25, we see that choice C is not true.

Since 400 = 20 x 20, we see that choice D is not true.

So choice E must be true. We can also show that it must be true because if n is odd, then k must be even, in order to produce an even product (400 is an even number). For example, if n is 25 (odd), then k must be even, which it is, since k must be 16.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If n and k are integers whose product is 400, which of the   [#permalink] 04 Feb 2019, 18:50
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