GMATPrep DS Variables Pos/Neg

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myfish: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Mon May 03, 2010 12:03 pm; Thanked: 3 times

by myfish » Sun Apr 08, 2012 4:33 pm

I tried to think this through but I am not sure. The first prompt means basically that either both x and y are positive or they are both negative. The second prompt means x > -y or y > -x. However, I get stuck with how to prove sufficiency from there. Anyone?

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Source: Beat The GMAT — Data Sufficiency | Sun Apr 08, 2012 4:33 pm

Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Sun Apr 08, 2012 5:03 pm

S1) As you said, both positive or both negative. Insufficient.

S2) To get a positive sum, we could add two positives, or we could add a positive and a negative (10 + -3 = 7, for instance). Insufficient.

Taken together, the only way both statements can be true is if both variables are positive. Thus, x must be positive. Sufficient.

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myfish: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Mon May 03, 2010 12:03 pm; Thanked: 3 times

by myfish » Sun Apr 08, 2012 5:20 pm

[quote="Bill@VeritasPrep"]S1) As you said, both positive or both negative. Insufficient.

S2) To get a positive sum, we could add two positives, or we could add a positive and a negative (10 + -3 = 7, for instance). Insufficient.

Taken together, the only way both statements can be true is if both variables are positive. Thus, x must be positive. Sufficient.[/quote]

Could you please elaborate on your last point? Or maybe show an algebraic way? Thanks so much.

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Sun Apr 08, 2012 5:25 pm

With two terms, we have three possible situations:

1. both positive
2. both negative
3. one positive, one negative

If we have two positive values, (say 4 and 2), they always have a positive product (8) and a positive sum (6).

Two negative values (-4 and -2) always have a positive product (8) and a negative sum (-6).

One positive and one negative (4 and -2) will always have a negative product (-8), but could have a positive or negative sum (4 + -2 = 2; -4 + 2 = -2).

Number properties are tested fairly often, so it's definitely worth spending some time memorizing them.

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myfish: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Mon May 03, 2010 12:03 pm; Thanked: 3 times

by myfish » Sun Apr 08, 2012 6:01 pm

I was in a way more difficult arena of algebra. Common sense + number properties is sometimes enough. Thanks so much. Its so easy, its almost embarrassing.

[quote="Bill@VeritasPrep"]With two terms, we have three possible situations:

1. both positive
2. both negative
3. one positive, one negative

If we have two positive values, (say 4 and 2), they always have a positive product (8) and a positive sum (6).

Two negative values (-4 and -2) always have a positive product (8) and a negative sum (-6).

One positive and one negative (4 and -2) will always have a negative product (-8), but could have a positive or negative sum (4 + -2 = 2; -4 + 2 = -2).

Number properties are tested fairly often, so it's definitely worth spending some time memorizing them.[/quote]

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Apr 08, 2012 6:07 pm

Question: Is x > 0?

(1) xy > 0
If x = -2, y = -1, xy = (-2)(-1) = 2 > 0. Here, x < 0.
If x = 2, y = 1, xy = (2)(1) = 2 > 0. Here, x > 0.
No definite answer; NOT sufficient.

(2) x + y > 0
If x = 5, y = 3, x + y = 5 + 3 = 8 > 0. Here x > 0.
If x = -5, y = 8, x + y = -5 + 8 = 3 > 0. Here x < 0.
No definite answer; NOT sufficient.

Combining (1) and (2), we know that xy > 0 and x + y > 0, which clearly implies both x and y are > 0 because if both x and y are < 0, then x + y will not be > 0.
So, x > 0; SUFFICIENT.

The correct answer is C.

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Sun Apr 08, 2012 6:32 pm

myfish wrote:I was in a way more difficult arena of algebra. Common sense + number properties is sometimes enough. Thanks so much. Its so easy, its almost embarrassing.

One big giveaway that number properties and logic are the way to go are when we have inequalities involving 0 on side. Essentially, the question is telling us that whatever's on the other side is positive or negative, so we should able to attack it without actually spending the time required to solve.

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