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abcd is even and positive

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Intern
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abcd is even and positive [#permalink] New post 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
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Joined: 07 Jun 2014
Posts: 4720
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: abcd is even and positive [#permalink] New post 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!
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Sandy
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Re: abcd is even and positive   [#permalink] 30 May 2017, 01:30
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