If y

Question

If y < x < z and xyz < 0, is xy > 0? 1) yz > 0 2) xz > 0

BrentGMATPrepNow · Accepted Answer

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: A Cheers, Brent

quantumliner · Answer

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

himanshu22 · Answer

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

chetan2u · Answer

Hi... CASE II does not exit.. Because for xyz to be NEGATIVE, y has to be -ive in all cases. Solution:- Given that xyz<0.. Two cases.. a) all three x,y and z are NEGATIVE b) only one is NEGATIVE and other two are POSITIVE.. AND if only one is NEGATIVE, it has to be the smallest value, which is y here So y is NEGATIVE for sure and NONE is 0 Let's see the statements... 1)yz>0... Since y is NEGATIVE, z will also be NEGATIVE.. As negative*negative = positive And z alone cannot be NEGATIVE, even x will be NEGATIVE then only xyz<0.. So xz>0 Suff 2) xz>0... Both x and z can be -ive, then xy will be>0 or both can be +ive, then xy will be<0.. Different answers possible Insufficient A

valardohaeris · Answer

A in my opinion.

If xyz<0 then 2 cases
1. Y<0
2. All <0

From statement 1. yz>0 means z is negative and hence case 2 is satisfied. So statement 2 is sufficient.

From statement 2.xz>0 gives no information of sign about x. Hence insufficient

Sent from my iPad using GMAT Club Forum

eddy8700 · Answer

If y < x < z and xyz < 0, is xy > 0?

1) yz > 0
2) xz > 0

lets evaluate
y < x < z and xyz < 0 this info is given and hold true

product of 3 numbers will be negative when all three are negative or either of them is negative
also
y < x < z
when all three negative above eq can hold true
but for single variable to be negative
+ve <+ve<-ve (never possible)
+ve <-ve<+ve(never possible)
only possible case is when y is negative

first statement
yz>0
both positive or both negative
if both are positive then x<0 for xyz<0 to hold true but x cannot be negative as per above
So all three are negative hence xy>0 Sufficient

St 2
xz > 0
both positive or both negative
so both can be positive and y can be negative above discussion
xy<0
all three can be negative and xy>0
Not sufficient

answer is A

Mo2men · Answer

If y < x < z and xyz < 0, is xy > 0?

Let test cases to achieve the info in prompt:

We need either 3 -ve numbers or 1 -ve number.

Case 1: -3 < -2 < -1 .....xyz < 0

Case 2: -3 < 2 < 3......xyz < 0

No other cases

1) yz > 0

Case 1 is viable, while case 2 is not viable.

X must be -ve........xy>0......Answer is always Yes

Sufficient

2) xz > 0

Both cases are viable.

X is either -ve or +ve

Insufficient

Answer: A

exc4libur · Answer

(1) sufic 
yz>0: y,z - - or + +
yxz: - (-) - xy>0
yxz: + (+) + invalid

(2) insufic 
xz>0: x,z - - or + +
yxz: (-) - - xy>0
yxz: (-) + + xy<0

Ans (A)

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If y < x < z and xyz < 0, is xy > 0?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions