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If a, b, and c are integers and a*b^2/c is a positive even

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If a, b, and c are integers and a*b^2/c is a positive even [#permalink]

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If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?

I. ab is even
II. ab > 0
III. c is even

A. I only
B. II only
C. I and II
D. I and III
E. I, II, and III
[Reveal] Spoiler: OA
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Re: ab^2/c is even? [#permalink]

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New post 26 Sep 2010, 13:43
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Orange08 wrote:
If a , b, and c are integers and \(a*b^2/c\)is a positive even integer, which of the following must
be true?


I. ab is even
II. ab > 0
III. c is even

I only
II only
I and II
I and III
I, II, and III


Given: \(\frac{a*b^2}{c}=even>0\) --> \(ab^2=c*even=even\) --> either \(a\) is even or \(b\) or both.

I. \(ab\) is even --> according to the above this must be true;

II. \(ab>0\) --> not necessarily true, \(b\) could be positive as well as negative (for example \(a=1\), \(c=1\) and \(b=-2\));

III. \(c\) is even --> not necessarily true, see above example.

Answer: A (I only).
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Re: ab^2/c is even? [#permalink]

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New post 28 Sep 2010, 07:22
Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.

I only.letter A
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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]

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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]

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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]

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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]

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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]

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New post 18 Apr 2017, 02:27
Option A

(a*(b^2))/c = Positive Even integer. Odd: O, Even: E & fraction: F.
i.e., a,b,c are Even or b is even, a & c are Odd or a is Even, b & c are odd.

I. ab is even : True
II. ab > 0 : May or May NOT be True. no information about b's value.
III. c is even : May or May not be True
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Re: If a, b, and c are integers and a*b^2/c is a positive even [#permalink]

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New post 20 Apr 2017, 16:43
Orange08 wrote:
If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?

I. ab is even
II. ab > 0
III. c is even

A. I only
B. II only
C. I and II
D. I and III
E. I, II, and III


We are given that (a*b^2)/c is a positive even integer. Therefore, a*b^2 must be even. (If a*b^2 is odd, (a*b^2)/c can’t ever be even.)

Now recall that the product of an even number and any integer is even, so either a or b, or both, must be even. Thus we see that ab must be an even integer. However, ab DOES NOT have to be greater than zero, since a could be -2 and b could be 1. Finally, we see that c does not have to be even, since a could be -2, b could be 1, and c = -1. Thus, only Roman numeral I must be true.

Answer: A
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Re: If a, b, and c are integers and a*b^2/c is a positive even   [#permalink] 20 Apr 2017, 16:43
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