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by DavidG@VeritasPrep » Tue Feb 07, 2017 4:54 am
Mo2men wrote:Is a + b < c - d?

(1) a + b < c
(2) a + b < -d
Each statement alone is clearly not sufficient. S1 tells us nothing about d and S2 tells us nothing about c. Together, we can sum the inequalities to get
2(a + b) < c- d or a + b < (c - d)/2.

Case 1: c-d = 2 and a + b = .5. (We can test these numbers because (c-d)/2 = 2/2 = 1, and .5 <1.) .5 is less than 2, so we get a YES to the original question.

Case 2: c-d = - 2 and a + b = -1.5. (We can test these numbers because (c-d)/2 = -2/2 = -1, and -1.5 <-1.) -1.5 is not less than -2, so we get a NO to the original question.

Because we can get a YES or a NO to the original question, the statements together are not sufficient, and the answer is E
Last edited by DavidG@VeritasPrep on Tue Feb 07, 2017 7:58 pm, edited 2 times in total.
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by Mo2men » Tue Feb 07, 2017 4:57 am
DavidG@VeritasPrep wrote:
Mo2men wrote:Is a + b < c - d?

(1) a + b < c
(2) a + b < -d
Each statement alone is clearly not sufficient. S1 tells nothing about d and S2 tells us nothing about c. Together, we can sum the inequalities to get
2(a + b) > c- d or a + b > (c - d)/2.

Case 1: c-d = 2 and a + b = 1.5. (We can test these numbers because (c-d)/2 = 2/2 = 1, and 1.5 >1.) 1.5 is not greater than 2, so we get a NO to the original question.

Case 2: c-d = 2 and a + b = 10. (We can test these numbers because (c-d)/2 = 2/2 = 1, and 10 >1.) 10 is greater than 2, so we get a YES to the original question.

Because we can get a YES or a NO to the original question, the statements together are not sufficient, and the answer is E
Why sign is reversed? It should be in same direction while adding two inequalities.
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by DavidG@VeritasPrep » Tue Feb 07, 2017 5:39 am
Why sign is reversed? It should be in same direction while adding two inequalities.
Because I have a small child who doesn't sleep well :)

The sign doesn't flip. I'll edit that post.
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by Mo2men » Tue Feb 07, 2017 11:16 am
DavidG@VeritasPrep wrote:
Mo2men wrote:Is a + b < c - d?

(1) a + b < c
(2) a + b < -d
Each statement alone is clearly not sufficient. S1 tells us nothing about d and S2 tells us nothing about c. Together, we can sum the inequalities to get
2(a + b) < c- d or a + b < (c - d)/2.

Case 1: c-d = 2 and a + b = .5. (We can test these numbers because (c-d)/2 = 2/2 = 1, and .5 <1.) .5 is not greater than 2, so we get a NO to the original question.

Case 2: c-d = - 2 and a + b = -1.5. (We can test these numbers because (c-d)/2 = -2/2 = -1, and -1.5 <-1.) -1.5 is greater than -2, so we get a YES to the original question.

Because we can get a YES or a NO to the original question, the statements together are not sufficient, and the answer is E
Dear David,

Thanks for your response.

It seems your baby did not sleep for long time :)

While you choose numbers and answer is E, the case 1 & case 2 answers to original questions should be reversed too.

a+b < c-d

In case 1 : c-d = 2 & a + b = 0.5......satisfying the condition correctly.so we get a YES to the original question.

In case 2 : c-d = -2 & a + b = -1.5......satisfying the condition correctly.so we get a NO to the original question.
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by [email protected] » Tue Feb 07, 2017 11:17 am
Hi Mo2men,

When dealing with these types of multiple variable inequality-based questions, it's worth noting that there are no restrictions on what the individual variables can be, so you have to think about more than just the obvious possibilities (re: positive integers). Many Test Takers would simply look at the prompt - and not do any work - and assume that the answer is C. However, a bit more work is needed...

We're asked if (A+B) is less than (C - D). This is a YES/NO question.

1) A + B < C

This tells us nothing about the value of D.
Fact 1 is INSUFFICIENT

2) A + B < -D

This tells us nothing about the value of C.
Fact 2 is INSUFFICIENT

Combined you should consider how "close" the values could be to one another and the fact that the variables could be NEGATIVE numbers...

IF....
A = -1
B = -1
C = -1
D = 0
Then (-2) IS less than (-1) and the answer to the question is YES

IF....
A = -1
B = -1
C = -1
D = 1
Then (-2) is NOT less than (-2) and the answer to the question is NO
Combined, INSUFFICIENT

Final Answer: E

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by DavidG@VeritasPrep » Tue Feb 07, 2017 7:57 pm
It seems your baby did not sleep for long time Smile

While you choose numbers and answer is E, the case 1 & case 2 answers to original questions should be reversed too.
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by Jay@ManhattanReview » Mon Feb 13, 2017 9:50 pm
Mo2men wrote:Is a + b < c - d?

(1) a + b < c
(2) a + b < -d
Hi Mo2men,

We see that each statement alone is clearly not sufficient.

S1 tells us nothing about d and S2 tells us nothing about c.

Together, we can sum the inequalities: 2(a + b) < c- d

We see that DOUBLE OF A NUMBER [2(a+b)] is less than ANOTHER NUMBER (c -d), thus the first NUMBER (a+b) would be less than the second NUMBER (c -d). This is true if we are dealing with positive numbers.

However, it's not necessarily true if the above NUMBERS are negatives. Insufficient.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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by Matt@VeritasPrep » Fri Mar 03, 2017 3:57 am
DavidG@VeritasPrep wrote:
It seems your baby did not sleep for long time Smile

While you choose numbers and answer is E, the case 1 & case 2 answers to original questions should be reversed too.
Yes. One of those days, my friend...
I'm right there with you, I've had to type my last dozen posts with one cat asleep on my left arm and another on my right. This glamorous, late night, work from home life ...
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