Positive & Negative Questions

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saadishah: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Nov 23, 2015 6:19 am; Thanked: 1 times

by saadishah » Wed Dec 02, 2015 3:13 am

If a-b/c < 0, is a > b?
(1) c < 0
(2) a + b < 0

I have two questions on this:

1. Can we rephrase the target question?
2. The solution is Statement#1 is SUFFICIENT, I only kind of get that. Can someone explain it that I 'get it'

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Source: Beat The GMAT — Data Sufficiency | Wed Dec 02, 2015 3:13 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Dec 02, 2015 4:00 am

saadishah wrote:If (a-b)/c < 0, is a > b?
(1) c < 0
(2) a + b < 0

(a-b)/c < 0 requires that (a-b) and c have DIFFERENT SIGNS.

Statement 1: c < 0
Since (a-b) and c must have different signs, (a-b) must be POSITIVE:
a - b > 0
a > b.
SUFFICIENT.

Statement 2: a + b < 0
It's possible that a=-1, b=0 and c=1, in which case a<b.
It's possible that a=0, b=-1 and c=1, in which case a>b.
INSUFFICIENT.

The correct answer is A.

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MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Wed Dec 02, 2015 4:08 am

saadishah wrote:If (a-b)/c < 0, is a > b?
(1) c < 0
(2) a + b < 0

I have two questions on this:

1. Can we rephrase the target question?

For a fraction to be < 0, it has to have either a positive numerator and a negative denominator or a negative numerator and a positive denominator.

So this question could be rephrased as "Is the fraction negative because a - b > 0 and c < 0 or because a - b < 0 and c > 0?"

If a - b > 0, then a > b. So that's the case we are looking for.

2. The solution is [spoiler]Statement#1 is SUFFICIENT[/spoiler], I only kind of get that. Can someone explain it that I 'get it'

Statement 1 tells us that c is negative. In that case, in order for the fraction (a-b)/c to be negative a - b must be positive. If a - b > 0 then a > b.

Sufficient.

Statement 2 could work with a variety of negative and positive numbers. It could be that a < b or that a > b.

So Statement 2 is insufficient, and the correct answer is B.

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Dec 11, 2015 2:05 pm

saadishah wrote:If a-b/c < 0, is a > b?
(1) c < 0
(2) a + b < 0

I have two questions on this:

1. Can we rephrase the target question?
2. The solution is Statement#1 is SUFFICIENT, I only kind of get that. Can someone explain it that I 'get it'

I think you're on to something with your first question.

We have (a - b)/c < 0, which is really

a/c - b/c < 0, or

a/c < b/c

To compare a and b, we need only to know the sign of c. If c is positive, when we multiply both sides by c we'll have a < b. But if c is NEGATIVE, when we multiply both sides by c, we'll have a > b.

So the question reduces to "Is c > 0 or < 0?" and we can easily answer with S1.

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