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17 Apr 2017, 08:39
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A
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Difficulty:
75%
(hard)
Question Stats:
50% (01:56) correct
50%
(02:03)
wrong
based on 732
sessions
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If y < x < z and xyz < 0, is xy > 0?
1) yz > 0
2) xz > 0
1) yz > 0
2) xz > 0
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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
17 Apr 2017, 19:37
Kudos
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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.
can someone explain on this?
Thanks
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.
can someone explain on this?
Thanks
