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Is t =|r - s|? (1) 3r > 3s (2) t = r -s

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Is t =|r - s|? (1) 3r > 3s (2) t = r -s  [#permalink]

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New post 22 Jan 2019, 00:47
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Is t =|r - s|?

(1) 3r > 3s

(2) t = r -s

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Is t =|r - s|? (1) 3r > 3s (2) t = r -s  [#permalink]

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New post 22 Jan 2019, 15:34
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Gmatprep550 wrote:
Is t =|r - s|?

(1) 3r > 3s

(2) t = r -s


First, we have to know that if r-s<0 so |r-s|=s-r and if r-s>=0; |r-s|=r-s

(1) 3r > 3s -> r-s>0 -> t=r-s but we don't have any value. Insufficient.

(2) t=r-s -> if is happens, so r-s must be >=0 to answer the question, but we don't have it in this point. Insufficient

Finally (1) and (2) are sufficient together, because if r-s>0, so t=r-s and we can confirm with the point (2).
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Re: Is t =|r - s|? (1) 3r > 3s (2) t = r -s  [#permalink]

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New post 30 Jan 2019, 11:02
@chetan2u:-can you please explain how this question needs to be solved?
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Re: Is t =|r - s|? (1) 3r > 3s (2) t = r -s  [#permalink]

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New post 30 Jan 2019, 12:07
Gmatprep550 wrote:
Is t =|r - s|?

(1) 3r > 3s

(2) t = r -s



(1) Nothing about t NS

(2) t = r-s. It is tempting to mark sufficient, but lets test some values Let r=-2 t=-3 then t =-2--3 =1 and |r-s| - |1| =1 Yes

let r=-2, s=1 then t =-2 - 1 =-3 and |r-s| =|-3| = 3 NS


(1) and (2) 3r>3s --> r>s And t=r-s Logic tells us that t will always be positive thus suff, however we can test some values just to be sure.

Notice for values of r and s r >S So, let r=-3, s=-4 then r-s = -3 --4 = 1 and |r-s| = |1| =1 Yes

Let r=-1/2 and s=-1 then r-s =1/2 and |r-s| =1/2 Yes

Let r=-1/2 s = -3/4 then r-s = 1/4 and |r-s| = |1/4| = 1/4 Yes

Let r = 1/2 s =1/4 then r-s = 1/4 and |r-s| = 1/4 Yes

Let r=2 and s=1 then r-s = 2-1 = 1 and |r-s| =|1| = 1

So whether we pick negative integers, negative fractions, positive fractions, or positive integers for r and s we get a Yes answer we can mark sufficient

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Re: Is t =|r - s|? (1) 3r > 3s (2) t = r -s  [#permalink]

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New post 30 Jan 2019, 12:27
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Manat,

the question asks if t =|r-s|.. note that the modulus is always non-negative. So, we can answer this question as yes or no, based on knowing if t = r-s or t = s-r depending on which of r & s is bigger.

For example, if r > s and t = r - s then we can say that yes, t = |r - s|, but it would be a certain "no" if r < s. Here, r - s would be negative and t cannot take a negative value.

Let us look at -

Statement (1)
3 r > 3s
or,
r > s ...does not give us any info to relate with t, hence insufficient

Statement (2)
t = r - s
This too is insufficient as depending on which one is bigger, r - s could either be negative or positive and hence we cannot be sure if t = |r - s|

Combining the two together - we can definitely say that t = |r-s| and that r-s is positive.

Hope this helps :-)
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Re: Is t =|r - s|? (1) 3r > 3s (2) t = r -s  [#permalink]

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New post 30 Jan 2019, 19:13
@Gladiator59:- Crystal clear. Thank you.
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Re: Is t =|r - s|? (1) 3r > 3s (2) t = r -s  [#permalink]

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New post 30 Jan 2019, 19:42
Gmatprep550 wrote:
Is t =|r - s|?

(1) 3r > 3s

(2) t = r -s



What's the source for this question?
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Re: Is t =|r - s|? (1) 3r > 3s (2) t = r -s  [#permalink]

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New post 30 Jan 2019, 23:25
dcwanderer30 wrote:
Gmatprep550 wrote:
Is t =|r - s|?

(1) 3r > 3s

(2) t = r -s



What's the source for this question?



Hi dcwanderer30,

Apologies as I don't know the source of above question as someone posted it in whatsapp study group and it was a nice question hence shared with this forum.
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Re: Is t =|r - s|? (1) 3r > 3s (2) t = r -s   [#permalink] 30 Jan 2019, 23:25
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