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# An even and an odd integer are multiplied together. Which of the follo

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Math Expert
Joined: 02 Sep 2009
Posts: 43862
An even and an odd integer are multiplied together. Which of the follo [#permalink]

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17 Apr 2015, 03:48
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Difficulty:

5% (low)

Question Stats:

81% (00:40) correct 19% (00:32) wrong based on 109 sessions

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An even and an odd integer are multiplied together. Which of the following could not be the square of their product?

(A) 36
(B) 100
(C) 144
(D) 225
(E) 400

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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17 Apr 2015, 04:03
Bunuel wrote:
An even and an odd integer are multiplied together. Which of the following could not be the square of their product?

(A) 36
(B) 100
(C) 144
(D) 225
(E) 400

Kudos for a correct solution.

36=$$6^2$$=2*3--->Possible
100=$$10^2$$=2*5--->Possible
144=$$12^2$$=4*3--->Possible
225=$$15^2$$=3*5--->Not Possible
400=$$20^2$$=4*5--->Possible

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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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18 Apr 2015, 10:19
1
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Expert's post
Hi All,

This is an example of a question that can be solved with Number Properties; NPs show up in a variety of questions on Test Day (including many DS questions), so putting some extra practice into this category is a good idea for most Test Takers.

Here, we're told to take the product of an EVEN integer and an ODD integer. (Even)(Odd) = Even. Next, we're asked to SQUARE that result. (Even)^2 = Even. The question asks for the answer that could NOT be the result of using these Number Properties as described. Since we know the end result MUST be Even, there's only one answer here that could NOT occur....

[Reveal] Spoiler:
D

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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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18 Apr 2015, 13:32
4
KUDOS
Product of an even and odd integer will at least be divisible by 2

So , if we square the product, then it will be at least divisible by 4

only 225, among the given list of nos is not divisible by 4 and hence is the reqd answer

Should be D
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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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18 Apr 2015, 23:20
$$even\,*\,odd\,=\,even$$
$$even^2\,*\,odd^2\,=\,even*(even\,*odd\,*odd)$$$$\,=\,even$$; resultant should be even
here $$225$$ is the odd one out

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Posts: 581
Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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19 Apr 2015, 02:22
1
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[quote="Bunuel"]An even and an odd integer are multiplied together. Which of the following could not be the square of their product?

(A) 36
(B) 100
(C) 144
(D) 225
(E) 400

2*3=6 and 6^2=36
5*2=10 and 10^2=100
3*4=12 and 12^2=144
5*4=20 and 20^2=400

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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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19 Apr 2015, 20:30
1
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Hi Bunuel,

I think there might be a mistake here, the GMAT timer is showing C as the correct answer, is the answer not D?
Math Expert
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Posts: 43862
Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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20 Apr 2015, 04:08
Bunuel wrote:
An even and an odd integer are multiplied together. Which of the following could not be the square of their product?

(A) 36
(B) 100
(C) 144
(D) 225
(E) 400

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

One way to approach this problem is to start with an even and an odd integer and plug them in to the parameters set by the problem. If we begin with two and three, we see that the product is six and the square of the product is thirty six.

(2)(3) = 6; 6^2 = 36

Similarly we can see that two and five, three and four, and four and five all give us possible answer choices.

(2)(5) = 10; 10^2 = 100

(4)(3) = 12; 12^2 = 144

(4)(5) = 20; 20^2 = 400

Answer choice (D) is also a perfect square, but if we take the square root of it, we see that the result is fifteen, which is not divisible by an even and an odd number. Thus the only answer that could not be the squared product of an even and odd integer is answer choice (D).
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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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20 Apr 2015, 04:09
1
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Expert's post
achilds wrote:
Hi Bunuel,

I think there might be a mistake here, the GMAT timer is showing C as the correct answer, is the answer not D?

Yes, the correct answer is D. Edited the OA in the original post. Thank you for noticing this.
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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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21 Apr 2015, 01:17
Bunuel wrote:
An even and an odd integer are multiplied together. Which of the following could not be the square of their product?

(A) 36
(B) 100
(C) 144
(D) 225
(E) 400

Kudos for a correct solution.

(A) 36 (1×6)^2
(B) 100 (1×10)^2
(C) 144 (1×12)^2
(D) 225(all factors are odd for this number , so this is our answer)
(E) 400(1×20)^2
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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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26 Apr 2015, 21:07
Bunuel wrote:
achilds wrote:
Hi Bunuel,

I think there might be a mistake here, the GMAT timer is showing C as the correct answer, is the answer not D?

Yes, the correct answer is D. Edited the OA in the original post. Thank you for noticing this.

This can be simply be done in a sec, even * odd always gives even, and even square is even, except 225 rest all are even
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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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15 May 2017, 18:39
even times odd should give us even result.

The only add answer choice, 225, 15 times 15 is odd and it couldn't be the multiplication of and odd and an even number.
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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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15 May 2017, 20:35
Bunuel wrote:
An even and an odd integer are multiplied together. Which of the following could not be the square of their product?

(A) 36
(B) 100
(C) 144
(D) 225
(E) 400

Kudos for a correct solution.

(even*odd)^2 = ?

Checking options

(A) 36 = 2^2*3^2 possible
(B) 100 = 2^2*5^2 Possible
(C) 144 = 2^4*3^2 Possible
(D) 225 = 3^2*5^2 NOT Possible as no even power of 2 is available
(E) 400

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Re: An even and an odd integer are multiplied together. Which of the follo [#permalink]

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15 May 2017, 21:18
Bunuel wrote:
An even and an odd integer are multiplied together. Which of the following could not be the square of their product?

(A) 36
(B) 100
(C) 144
(D) 225
(E) 400

Kudos for a correct solution.

Did not take much time, simply scanned the values as Even or Odd and there it was D.

Plugging numbers is a good way to cross check and still worth doing it considering scanning of numbers did not take much time.
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Re: An even and an odd integer are multiplied together. Which of the follo   [#permalink] 15 May 2017, 21:18
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