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adding inequalities- doubt

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adding inequalities- doubt

by ahahkhyati.j » Thu Oct 22, 2015 5:39 am
Hi, Can someone please help

Is p+q > r+s?

(1) p>r+s
(2) q>r+s

Ans: E



I clearly know that the two statements individually are insufficient but for combining the two statements can i add the inequalities here? If i do so i get ans C. While if i try to take negative and positive values i get E Can someone please explain. Thanks.
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by DavidG@VeritasPrep » Thu Oct 22, 2015 5:58 am
ahahkhyati.j wrote:Hi, Can someone please help

Is p+q > r+s?

(1) p>r+s
(2) q>r+s

Ans: E



I clearly know that the two statements individually are insufficient but for combining the two statements can i add the inequalities here? If i do so i get ans C. While if i try to take negative and positive values i get E Can someone please explain. Thanks.
So long as the inequality signs are facing the same direction, it's valid to sum the inequalities. When we do, we get: q + p > 2(r+s); We haven't proved anything yet because we're asked about the relationship between q +p and r +s, not about the relationship between q + p and 2(r+s). So even after summing the inequalities, I'd still be inclined to test values.

Say that q + p = 3 and r + s = 1. It's true that q + p > 2(r+s), so we can test these numbers. And q +p > r +s, so we get a YES to the question

Now say that q + p = -3 and r + s = -2. It's true that q + p > 2(r+s) because -3 > -4, so we can test these numbers. Now q +p < r +s, as -3 < -2, so we get a NO to the question.

So the answer is E
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by ahahkhyati.j » Thu Oct 22, 2015 6:08 am
Sorry got my mistake. thanks a ton for replying.
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by Brent@GMATPrepNow » Thu Oct 22, 2015 9:16 am
Here's a free video that explains the different ways in which we can combine inequalities - https://www.gmatprepnow.com/module/gmat- ... /video/982

Here are two questions to practice with:
- https://www.gmatprepnow.com/module/gmat- ... /video/983
- https://www.gmatprepnow.com/module/gmat- ... /video/984

Cheers,
Brent
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by [email protected] » Thu Oct 22, 2015 10:13 am
Hi ahahkyati.j,

Certain DS questions on Test Day are really meant to test the 'thoroughness' of your thinking. Often, in those situations , you have to think about the 'less obvious' possibilities (negatives, fractions, etc.) to get to the correct answer.

In this prompt, "R+S" appears as a combined-term, so I'm going to show you how to TEST VALUES in this scenario (and how to take advantage of that pattern). Since you're already clear on why each statement is insufficient on its own, I'm going to jump straight to the last couple of steps in this question.

IF....
R+S = -2

Then both P and Q have to be greater than -2.... How MUCH greater depends on you, but ANYTHING greater than -2 is something that you have to consider.

IF...
P = 10
Q = 10
Then the answer to the question is.... Is 10+10 > -2? .....YES.

IF....
P = -1
Q = -1
Then the answer to the question is.... Is -1 + -1 > -2? .... NO.

Combined, INSUFFICIENT

Final Answer: E

Ultimately it doesn't take much work to get to the correct answer, but that work is easier to do if you physically write everything on the pad, so that you can 'see' the work and better consider the various possibilities.

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Rich
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