Tricky Number Properties: If (a-b)/c<0, is a>b?

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amirhakimi: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Oct 14, 2013 11:48 pmFollowed by: 1 member; Thanked: 5 times

by amirhakimi » Fri Nov 01, 2013 3:02 am

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

Answer is A

Why (1) is sufficient
[spoiler]If c<0, a-b>0 --> a>b
Sufficient![/spoiler]

Why (2) is [spoiler] not sufficient?[/spoiler]

Here is the tip: [spoiler]If a+b<0, it can be inferred that a<-b. By multiplying both sides by (-1), -a>b. There is no way to determine if a>b or not.
Take a as (-2) and b as (+1){which means a<b}, -(-2)>1
Take a as (-1) and b as (-2){which means a>b}, -(-1)>-2
Not sufficient![/spoiler]

Last edited by amirhakimi on Fri Nov 01, 2013 3:45 am, edited 2 times in total.

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Source: Beat The GMAT — Data Sufficiency | Fri Nov 01, 2013 3:02 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 » Fri Nov 01, 2013 3:31 am

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

Statement 1: c<0
Since c<0, we must FLIP the inequality when we multiply by c:
(a-b)/c < 0
(a-b)/c * c > 0 * c
a-b > 0
a>b.
SUFFICIENT.

Statement 2: a+b < 0
Statement 1 offers a CLUE.
Test one case where c<0 and one case where c>0.

Case 1: a=-1, b=-2 and c=-1
Statement 2 and the constraint in the question stem are both satisfied:
a+b = -1 + (-2) = -3.
(a-b)/c = [-1 - (-2)]/-1 = -1.
In this case, a>b.

Case 2: a=-2, b=-1, and c=1
Statement 2 and the constraint in the question stem are both satisfied:
a+b = -2 + (-1) = -3.
(a-b)/c = [-2 - (-1)]/1 = -1.
In this case, a<b.

Since a>b in Case 1, but a<b in Case 2, INSUFFICIENT.

The correct answer is A.

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Fri Nov 01, 2013 7:30 am

(a-b)/c < 0

To find: a>b

Statement 1:
c < 0
So, (a-b) must be positive +
Therefore, a > b
SUFFICIENT

Statement 2:
a + b < 0
A & B can take up any value; Also, we have no info about "c"
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]

R A H U L

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by [email protected] » Fri Nov 01, 2013 6:04 pm

Hi arirhakimi,

Many DS questions are based on "number properties" - the little rules behind odds/evens, positives/negatives, integers/non-integers, etc.

Here, we're asked if a > b? This is a YES/NO question.

We're told that [a-b]/c < 0

With THAT information, you can make a BIG deduction immediately: there are only two possibilities for the numerator and denominator.

[a-b] = positive and c = negative

OR

[a-b] = negative and c = positive

Fact 1: c < 0

Since c is negative, that means that [a-b] MUST be positive. Therefore, a MUST be > b.
The answer to the question is YES.
Fact 1 is SUFFICIENT

Fact 2: a + b < 0

This tells us that one, the other, or both a and b are negative. But we don't know their relative values and we don't know which is bigger.
A might be > b
B might be > a
Fact 2 is INSUFFICIENT

Final Answer: A

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