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# Is t=|r−s|?

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Math Expert
Joined: 02 Sep 2009
Posts: 52385

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29 Apr 2016, 01:45
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Difficulty:

35% (medium)

Question Stats:

61% (01:14) correct 39% (01:24) wrong based on 168 sessions

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Is t=|r−s|?

(1) 3r > 3s
(2) t=r−s

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Math Expert
Joined: 02 Aug 2009
Posts: 7211
Re: Is t=|r−s|?  [#permalink]

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29 Apr 2016, 02:57
Bunuel wrote:
Is t=|r−s|?

(1) 3r > 3s
(2) t=r−s

what all does Is t=|r-s| means?
1) is t a positive number..
2) is the numeric value of t equal to the difference/ distance between r and s?

lets see the statements-

(1) 3r > 3s
or 3(r-s)>0..
so we know r-s>0, but NOTHING about t..
Insuff..

(2) t=r−s
Likely to be choosen as Suff by few..
But we do not know which is greater ..
a) if r> s, r-s >0 and t will be positive.. ans will be YES
b) if s>r, r-s<0 so t<0.. ans will be NO
Insuff

combined..
we know r-s>0 and from II that r-s = t..
so t=|r-s|
suff
C
_________________

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

GMAT online Tutor

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Joined: 19 Jun 2017
Posts: 4
Re: Is t=|r−s|?  [#permalink]

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17 Apr 2018, 12:42
What if both r and s are negative?
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1434
Location: India
Re: Is t=|r−s|?  [#permalink]

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18 Apr 2018, 04:23
irynalowry wrote:
What if both r and s are negative?

Hello

Even if both r and s are negative, first statement tells us that r > s. And second statement tells us that t = r-s. Now even if both r and s are negative, if r > s then r - s will be positive only (you can try taking negative values of r/s such that r > s and check).

So after combining the statements, we know 't' or 'r-s' is positive and equal and thus t = |r-s|
Intern
Joined: 19 Jun 2017
Posts: 4
Re: Is t=|r−s|?  [#permalink]

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19 Apr 2018, 17:50
I got it now. Combining 1st and 2nd, the difference will always be positive because of the first statement.

Thank you
Re: Is t=|r−s|? &nbs [#permalink] 19 Apr 2018, 17:50
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# Is t=|r−s|?

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