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# Is |r|*s = |s|*r?

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Math Expert
Joined: 02 Aug 2009
Posts: 7108

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28 Jun 2018, 20:17
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Difficulty:

25% (medium)

Question Stats:

76% (01:10) correct 24% (01:29) wrong based on 96 sessions

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Is |r|*s = |s|*r?

(1) rs > 0
(2) $$r^2=s^2$$

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is |r|*s = |s|*r?  [#permalink]

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28 Jun 2018, 20:36
chetan2u wrote:
Is |r|*s = |s|*r?

(1) rs > 0
(2) $$r^2=s^2$$

New question

Using A: Yes. rs>0 means both are same sign.
Using B: No. $$r^2=s^2$$ means |r| = |s|. But r and s may have opposite signs, so No.
CR Forum Moderator
Joined: 25 Apr 2018
Posts: 356
Re: Is |r|*s = |s|*r?  [#permalink]

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28 Jun 2018, 20:39
I think its A

1 implies both r and s have the same sign so |r|.s and |s|.r will yield the same result.

2 implies that they can have different signs.It may be yes or no.

+1 if this helps!

chetan2u wrote:
Is |r|*s = |s|*r?

(1) rs > 0
(2) $$r^2=s^2$$

New question

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Joined: 14 Dec 2017
Posts: 518
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28 Jun 2018, 21:02
chetan2u wrote:
Is |r|*s = |s|*r?

(1) rs > 0
(2) $$r^2=s^2$$

New question

Statement 1: $$rs > 0$$

$$r > 0, s > 0$$ or $$r < 0, s < 0$$

$$r$$ & $$s$$ have the same sign

$$r = 1, s = 2$$, we get YES as answer

$$r = -1, s = -2$$, we get YES as answer.

Statement 1 is Sufficient.

Statement 2: $$r^2=s^2$$

r & s can take any sign or both are equal to 0

$$r = 0, s = 0$$. we get YES as answer

$$r = 1, s = -1$$, we get NO as answer

Statement 2 is Not Sufficient.

Thanks,
GyM
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Is |r|*s = |s|*r? &nbs [#permalink] 28 Jun 2018, 21:02
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