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# abcd is even and positive

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Intern
Joined: 17 May 2017
Posts: 2
GRE 1: Q163 V161
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abcd is even and positive [#permalink]  29 May 2017, 19:22
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abcd is even and positive, and abc is odd and positive

Quantity A
1

Quantity
d

A) Quantity A is greater
B) Quantity B is greater
C) The two quantities are equal
D) The relationship cannot be determined from the information given
[Reveal] Spoiler: OA
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1820 [2] , given: 397

Re: abcd is even and positive [#permalink]  30 May 2017, 01:30
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Expert's post
We know that $$abc$$ is odd and positive and since odd and positive are properties of integers it is safe to say $$abc$$ is an integer.

Further more $$abcd$$ is even which $$d$$ is an even integer.

For example:

a=1, b = 3 , c=9 and d=2 so abc=27 and abcd=54.

Here d=2 or any even number greater than 2.

It is also possible that $$d= \frac{1}{a}$$ or $$d= \frac{1}{b}$$ or $$d= \frac{1}{b}$$

That would make $$abcd = bc$$ or$$abcd = ac$$ or $$abcd = ab$$ respectively.

So $$abc$$ is odd

$$b= 1$$ $$c=\frac{1}{2}$$ $$a=2$$ and $$d=\frac{1}{a}= \frac{1}{2}$$

$$abc=1$$ and $$abcd=2$$

Clearly d can be a fraction as well.

Hence D is the correct option!
_________________

Sandy
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Re: abcd is even and positive   [#permalink] 30 May 2017, 01:30
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