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

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

Answer: D

[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

Answer D

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.

\(even\,*\,odd\,=\,even\)
\(even^2\,*\,odd^2\,=\,even*(even\,*odd\,*odd)\)\(\,=\,even\); resultant should be even
here \(225\) is the odd one out

Answer D

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).

(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

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

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.

(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

Answer: Option D

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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