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Is xyz > 0 ? (1) (x - 3)(y - 3) > 0 (2) z > 0
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27 Mar 2022, 08:11
27 Mar 2022, 08:11
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00:00
A
B
C
D
E
Difficulty:
45%
(medium)
Question Stats:
54% (01:23) correct
46%
(01:32)
wrong
based on 41
sessions
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Is xyz>0 a) (x-3) (y-3)>0 b)z>0
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Updated on: 27 Mar 2022, 08:55
Updated on: 27 Mar 2022, 08:55
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Target is
xyz>0
possible when all x,y & z are +ve or when either of two are -ve and other +ve
#1
(x-3) (y-3)>0
possible when both x,y are +ve and >3 or else
x,y are both -ve
insufficient as z is not known
#2
z>0
but no info about x,y insufficient
from 1 &2
we know that z is +ve
but x,y can be +ve but have to be >3 or can both x,y can be -ve
in either cases xyz will be >0
Also possible that either of x or y is + but <3 and other is - ve
Insufficient
option E
Is xyz>0
a) (x-3) (y-3)>0
b)z>0
xyz>0
possible when all x,y & z are +ve or when either of two are -ve and other +ve
#1
(x-3) (y-3)>0
possible when both x,y are +ve and >3 or else
x,y are both -ve
insufficient as z is not known
#2
z>0
but no info about x,y insufficient
from 1 &2
we know that z is +ve
but x,y can be +ve but have to be >3 or can both x,y can be -ve
in either cases xyz will be >0
Also possible that either of x or y is + but <3 and other is - ve
Insufficient
option E
Is xyz>0
a) (x-3) (y-3)>0
b)z>0
Originally posted by Archit3110 on 27 Mar 2022, 08:22.
Last edited by Archit3110 on 27 Mar 2022, 08:55, edited 1 time in total.
Last edited by Archit3110 on 27 Mar 2022, 08:55, edited 1 time in total.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Given Kudos: 91
Q51 V47
Re: Is xyz > 0 ? (1) (x - 3)(y - 3) > 0 (2) z > 0
[#permalink]
27 Mar 2022, 08:52
27 Mar 2022, 08:52
3
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1
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Expert Reply
SelimAIUB wrote:
Is xyz>0
a) (x-3) (y-3)>0
b)z>0
a) (x-3) (y-3)>0
b)z>0
We'll need information about the signs of all three letters, so the answer could only be C or E. Using both Statements, we know from Statement 2 that z is positive, so all we need to know is whether xy is positive. Statement 1 tells us that x-3 and y-3 have the same sign. If they're both positive, then x > 3 and y > 3, and x and y are both positive, so xy is positive. But if x-3 and y-3 are both negative, and x < 3 and y < 3, it is then possible for x and y to have opposite signs. It might be true, say, that x = 2 and y = -10. In that case, xy can be negative. So we can't be sure if xy is positive or negative, and the answer is E.
