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Difficulty:
95%
(hard)
Question Stats:
37% (02:30) correct
63%
(02:14)
wrong
based on 132
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For any numbers W and Z, W∙Z=Wˆ3 * Z(8-Wˆ2) . If both Z and W∙Z are positive numbers, which of the following could be a value of W ?
(A) 9
(B) 3
(C) 0
(D) -2
(E) -9
(A) 9
(B) 3
(C) 0
(D) -2
(E) -9
24 Dec 2015, 20:18
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sara86
Hi,
it is given that both Z and W•Z are positive numbers and \(W•Z=Wˆ3 Z(8-Wˆ2)\)..
this means Wˆ3 Z(8-Wˆ2) must be positive..
we know Z is positive, so Wˆ3 *(8-Wˆ2) must be positive...
in other words, Wˆ3 and (8-Wˆ2) must be of the same sign..
lets see the two cases ..
1) Both positive..
W^3 is positive, so 8-W^2>0..
or W^2<8....or W < 3 as 3^2=9...
eliminate 9 and 3 that is A and B...
2) both negative..
W^3 is negative, so 8-W^2<0..
or W^2>8....or W <- 2 or W>2..
W>2 can be discarded as here W is taken as negative
D can be eliminated since it is -2,
E is the answer..
Note :- C which is 0 can be eliminated initially itself as W.Z will become 0 in that case.
and after initial steps We can substitute the values and find the answer, especially so, since it is asking " which of the following could be a value of W ?".
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
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24 Dec 2015, 20:43
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chetan2u
IMO, W can not be <0 in this question as it is given that both z and w*z are >0 ---> w>0. The question needs to be reformatted as it is mentioning W and w and the RHS is not clearly written.
