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# If (r+t)/(r-t)>0, is r>t?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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06 Jun 2016, 22:34
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Difficulty:

95% (hard)

Question Stats:

43% (01:57) correct 57% (01:25) wrong based on 101 sessions

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If (r+t)/(r-t)>0, is r>t?
1) t>0
2) r>0

*An answer will be posted in 2 days.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 18 Jan 2010 Posts: 254 Re: If (r+t)/(r-t)>0, is r>t? [#permalink] ### Show Tags 07 Jun 2016, 06:35 4 MathRevolution wrote: If (r+t)/(r-t)>0, is r>t? 1) t>0 2) r>0 *An answer will be posted in 2 days. The question can be rewritten as: $$\frac{(r+t)}{(r-t)}$$>0 Now this is possible when either both numerator and denominator are positive. or both numerator and denominator are negative Case 1: r+t > 0 r-t > 0 Add these two: 2r> 0; r > 0 --> This is my new question. Show that r> 0 Case 1: r+t < 0 r-t < 0 Add these two: 2r < 0; r < 0 --> This is my new question. Show that r < 0 So if there is any option that shows that r > 0 or less than 0 --> I can get answer. Statement 1 Gives no idea about r. Not sufficient. Statement 2 We got our answer. r > 0 This means I can say that r+t > 0 (r > -t) r-t > 0 (r > t) --> This is what we wanted to show. Unique answer obtained. B is the answer. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6227 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If (r+t)/(r-t)>0, is r>t? [#permalink] ### Show Tags 08 Jun 2016, 16:59 We can modify the original condition and the question. From (r+t)/(r-t)>0, we get r-t>0? and r+t>0?. If we add two questions together, the question becomes 2r>0?. Hence, r>0?. Then, the condition 2) becomes ‘yes’ and it is sufficient. Hence, the correct answer is B. - Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If (r+t)/(r-t)>0, is r>t?  [#permalink]

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30 Jul 2016, 18:25
Hi!
A nice one on how to further solve the question itself...

kindly share some brief notes on equality ...and absolute values please.
thanks
Intern
Joined: 21 Feb 2018
Posts: 16
Re: If (r+t)/(r-t)>0, is r>t?  [#permalink]

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03 Jul 2018, 17:31
I took the longer route and I think the answer is D
Taking the cases whether r>0 or t>0, we see that if r and t are on opposite sides of 0, it is already determined whether r>t. We have to determine in cases when both r and t are positive or negative.

Case 1:
r>0, t>0
=> r+t > 0
=> r-t has to be more than zero as well. => r > t. Determined

Case 2:
r<0, t<0
=> r+t < 0
=> r-t has to be less than zero as well.
=> r<t. Determined.

I therefore find that Either statement is sufficient for determination of whether r>t or not.
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Re: If (r+t)/(r-t)>0, is r>t?  [#permalink]

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03 Jul 2018, 21:49
slayer1983 wrote:
I took the longer route and I think the answer is D
Taking the cases whether r>0 or t>0, we see that if r and t are on opposite sides of 0, it is already determined whether r>t. We have to determine in cases when both r and t are positive or negative.

Case 1:
r>0, t>0
=> r+t > 0
=> r-t has to be more than zero as well. => r > t. Determined

Case 2:
r<0, t<0
=> r+t < 0
=> r-t has to be less than zero as well.
=> r<t. Determined.

I therefore find that Either statement is sufficient for determination of whether r>t or not.

Hello

I think in first statement we are ignoring one thing here.
If say t > 0, then we CAN have a case where r < 0 and still (r+t)/(r-t) > 0.
Eg, take t = 2 and r = -3. So r+t = 2-3 which is negative, and r-t = -3-2 which is also negative. So (r+t)/(r-t) = negative/negative which is positive. And here r < t.
Thats why statement 1 is NOT sufficient to answer the question.
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Joined: 21 Feb 2018
Posts: 16
Re: If (r+t)/(r-t)>0, is r>t?  [#permalink]

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03 Jul 2018, 21:54
amanvermagmat wrote:
slayer1983 wrote:
I took the longer route and I think the answer is D
Taking the cases whether r>0 or t>0, we see that if r and t are on opposite sides of 0, it is already determined whether r>t. We have to determine in cases when both r and t are positive or negative.

Case 1:
r>0, t>0
=> r+t > 0
=> r-t has to be more than zero as well. => r > t. Determined

Case 2:
r<0, t<0
=> r+t < 0
=> r-t has to be less than zero as well.
=> r<t. Determined.

I therefore find that Either statement is sufficient for determination of whether r>t or not.

Hello

I think in first statement we are ignoring one thing here.
If say t > 0, then we CAN have a case where r < 0 and still (r+t)/(r-t) > 0.
Eg, take t = 2 and r = -3. So r+t = 2-3 which is negative, and r-t = -3-2 which is also negative. So (r+t)/(r-t) = negative/negative which is positive. And here r < t.
Thats why statement 1 is NOT sufficient to answer the question.

Hi,
If we are considering this case when t>0 and r<0, then we are already establishing that r<t.
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Re: If (r+t)/(r-t)>0, is r>t?  [#permalink]

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03 Jul 2018, 22:04
slayer1983 wrote:
amanvermagmat wrote:
slayer1983 wrote:
I took the longer route and I think the answer is D
Taking the cases whether r>0 or t>0, we see that if r and t are on opposite sides of 0, it is already determined whether r>t. We have to determine in cases when both r and t are positive or negative.

Case 1:
r>0, t>0
=> r+t > 0
=> r-t has to be more than zero as well. => r > t. Determined

Case 2:
r<0, t<0
=> r+t < 0
=> r-t has to be less than zero as well.
=> r<t. Determined.

I therefore find that Either statement is sufficient for determination of whether r>t or not.

Hello

I think in first statement we are ignoring one thing here.
If say t > 0, then we CAN have a case where r < 0 and still (r+t)/(r-t) > 0.
Eg, take t = 2 and r = -3. So r+t = 2-3 which is negative, and r-t = -3-2 which is also negative. So (r+t)/(r-t) = negative/negative which is positive. And here r < t.
Thats why statement 1 is NOT sufficient to answer the question.

Hi,
If we are considering this case when t>0 and r<0, then we are already establishing that r<t.

Hello

Yes, but from first statement, there is another possibility: t>0 and r>0. Eg, if we take t = 4, r = 5: then r+t = 9 and r-t = 1, and 9/1 is also positive.
Here t > 0 and r > t.

So in my previous example (previous comment) t>0 while r<0 (so r is less than t)
And in my current example above, t>0 and r>0 (and r is greater than t)
Thats why this statement 1 is NOT sufficient to answer the question.
Re: If (r+t)/(r-t)>0, is r>t? &nbs [#permalink] 03 Jul 2018, 22:04
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