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# If a, b, and c are integers and ab^2/c is a positive even in

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Intern
Joined: 16 Jan 2013
Posts: 30
Concentration: Finance, Entrepreneurship
GMAT Date: 08-25-2013
If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

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Updated on: 20 Jun 2013, 00:50
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If a, b, and c are integers and ab^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

Originally posted by Countdown on 20 Jun 2013, 00:04.
Last edited by Bunuel on 20 Jun 2013, 00:50, edited 1 time in total.
Renamed the topic, edited the question and the tags.
Intern
Joined: 26 May 2010
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20 Jun 2013, 00:14
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Countdown wrote:

If a , b, and c are integers and ab2 / 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

ab2/c is positive which means a and C >0 or a and c<0 since b2 is positive
Case 1 - a=3 b=2 c=3 or c=6 where ab2 /2 would be even when c= 3 or c=6
lets see III option where C is even as per our assumption C can be even and odd, hence it is out.
lets see option II ab>0 a and b can positive or negative hence sign of ab cannot be determined hence it is out

So options B,C,D,E are gone and ans is A

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Senior Manager
Joined: 28 Apr 2012
Posts: 300
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31
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20 Jun 2013, 00:26
2
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Countdown wrote:

If a , b, and c are integers and ab2 / 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

I believe the expression is $$ab^2/c$$ is a positive integer.
Now we know,

1. even * even = even (2*4 = 8)
2. even * odd = even (2*3 = 6)
3. even / even = even or odd (8/2 = 4 , 6/2 = 3)
4. even / odd = even (6/3 = 2)
5. odd * odd = odd
6. odd / odd = odd (if the are divisible)
7. odd / even = <not divisible> as the denominator will always have an extra 2.

Coming back to my question, my result is even. Hence my numerator must be even, as odd numerator can never give even result. (we are considering divisible integers only)

$$ab^2$$ is even, hence either a is even or $$b^2$$ is even. If $$b^2$$ is even then b is even. Hence ab = even. (I) is true.
now $$\sqrt{b^2}$$ = +/- b, so ab can be > 0 or < 0, (II) is false
From rule 3 and 4, c can be even or odd. so (III) is false.

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Math Expert
Joined: 02 Sep 2009
Posts: 45455
Re: If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

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20 Jun 2013, 01:11
Countdown wrote:
If a, b, and c are integers and ab^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

Given: a, b, and c are integers and ab^2/c is a positive even integer.

Evaluate each option:

I. ab is even.

ab^2/c to be positive even integer ab^2 must be even, from which it follows that either a or b must be even, thus ab has to be even.

II. ab > 0

Since b is squared in our expression, then we can say nothing about its sign, thus we cannot say whether ab is positive.

III. c is even

The easiest one: ab^2/c = integer/c = even --> c could be even as well as odd.

P.S. Please read carefully and follow: 11-rules-for-posting-133935.html Pay attention to the rules #3 and 10. Thank you.
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Joined: 02 Sep 2016
Posts: 745
If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

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03 Apr 2017, 04:39
ab^2/c is an even integer.
When is that possible:
When b^2 or b is even (If b is even then b^2 would be even i.e. even*even is even. For example, 2*2=4)

a and c can either be even or odd. Why? Because an odd number can have an even multiple (e.g. 12 is multiple of 3). Also in 12, the first digit is odd and then also the number is even because it ends with an even digit.

Check the options:
(1) ab is even. YES!! Because we know b is even. So odd*even=even (e.g. 3*2=6) or even*even=even (e.g. 2*2=4)
(2) ab>0. Well!! It can be or can't be. Because ab^2/c is a positive integer. That tells us a few things:
- If b is negative, then b^2 is positive. And a and c are positive. In this case, ab will be less than 0.
- If a is negative and b is also negative, then ab>0 (negative*negative= positive). In this case ab>0. (Can eliminate this choice here only as we know that we are not getting a unique answer).
- If b is not negative and c and a are negative, then ab will be less than zero.

(3) c is even.
We already know that c can be odd or even.
And in mUST BE TRUE questions, there SHOULD be ONLY one answer.

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Joined: 09 Sep 2013
Posts: 6858
Re: If a, b, and c are integers and ab^2/c is a positive even in [#permalink]

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07 Apr 2018, 05:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a, b, and c are integers and ab^2/c is a positive even in   [#permalink] 07 Apr 2018, 05:49
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