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If y < x < z and xyz < 0, is xy > 0?
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17 Apr 2017, 08:39
17 Apr 2017, 08:39
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GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Given Kudos: 799
Location: Canada
If y < x < z and xyz < 0, is xy > 0?
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18 Apr 2017, 07:37
18 Apr 2017, 07:37
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GMATPrepNow wrote:
If y < x < z and xyz < 0, is xy > 0?
1) yz > 0
2) xz > 0
1) yz > 0
2) xz > 0
Target question: Is xy > 0?
Given: y < x < z and xyz < 0
If xyz < 0, then there are only TWO POSSIBLE CASES:
case a: all 3 numbers are negative (x, y and z are all NEGATIVE)
case b: 1 number is negative and the other 2 numbers are positive. Since y < x < z, then it must be the case that y is NEGATIVE, and x and z are POSITIVE
Statement 1: yz > 0
Let's compare this information with our given information.
The statement 1 information satisfies the conditions in case a. Reason: In case a, y and z are both negative, so yz > 0. So, case a IS possible
Conversely, this same information does not satisfy the conditions in case b. Reason: In case b, y is negative and z is positive, so yz < 0. So, case b is NOT possible
Since only case a is possible, we can be certain that x, y and z are all NEGATIVE, which means xy > 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: xz > 0
We'll compare this information with our given information.
The statement 2 information satisfies the conditions in case a. Reason: In case a, y and z are both negative, so xz > 0. So, case a IS possible
This information ALSO satisfies the conditions in case b. Reason: In case b, x and z are both positive, so xz > 0. So, case b IS possible
So, BOTH cases are possible.
In case a, x, y and z are all NEGATIVE, which means xy > 0
In case b, y is negative and x and z are positive, which means xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer:
Cheers,
Brent
General Discussion
Re: If y < x < z and xyz < 0, is xy > 0?
[#permalink]
17 Apr 2017, 08:58
17 Apr 2017, 08:58
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If y < x < z and xyz < 0, is xy > 0?
As xyz < 0, we know that either x,y, & z are all negative or only y is negative.
Question asks whether xy > 0, which basically means whether only y is negative?
1) yz > 0
Case 1, both y and z are negative.
In this case x also becomes negative. therefore xy is positive.
Case 2. both y and z are positive.
In this case the original condition x*y*z < 0 does not hold true, hence this case is not possible.
As only 1 case is possible, this statement is sufficient.
2) xz > 0
Case 1
Both x and z are negative and y is also negative, so x*y becomes positive
Case 2
Only x and z are positive and y is negative, so x*y becomes negative
As there are two possibilities, this statement is not sufficient.
Answer is A
As xyz < 0, we know that either x,y, & z are all negative or only y is negative.
Question asks whether xy > 0, which basically means whether only y is negative?
1) yz > 0
Case 1, both y and z are negative.
In this case x also becomes negative. therefore xy is positive.
Case 2. both y and z are positive.
In this case the original condition x*y*z < 0 does not hold true, hence this case is not possible.
As only 1 case is possible, this statement is sufficient.
2) xz > 0
Case 1
Both x and z are negative and y is also negative, so x*y becomes positive
Case 2
Only x and z are positive and y is negative, so x*y becomes negative
As there are two possibilities, this statement is not sufficient.
Answer is A
