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# If y(y − 3)(y + 2)(y − 1) = 0, is y negative?

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Manager
Joined: 02 Mar 2018
Posts: 70
Location: India
GMAT 1: 640 Q51 V26
GPA: 3.1
If y(y − 3)(y + 2)(y − 1) = 0, is y negative?  [#permalink]

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29 Jul 2018, 06:46
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65% (hard)

Question Stats:

56% (01:43) correct 44% (02:12) wrong based on 43 sessions

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If y(y − 3)(y + 2)(y − 1) = 0, is y negative?

(1) y^2 − 3y ≠ 0
(2) y^2 − 3y + 2 ≠ 0
Math Expert
Joined: 02 Aug 2009
Posts: 7036
Re: If y(y − 3)(y + 2)(y − 1) = 0, is y negative?  [#permalink]

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29 Jul 2018, 07:23
If y(y − 3)(y + 2)(y − 1) = 0, is y negative?
Possible values of y are one or more of 0,1,3 and -2..
So the question asks is y=-2?

(1) y^2 − 3y ≠ 0
So y(y-3) ≠ 0...
y is not 0 or 3..
But y can be 1 or -2
Insufficient

(2) y^2 − 3y + 2 ≠ 0
(y-2)(y-1) ≠ 0
So y is not 1 or 2
But y can be 0,3 or -2
Insufficient

Combined
y can be only -2
Sufficient

C
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If y(y − 3)(y + 2)(y − 1) = 0, is y negative?  [#permalink]

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29 Jul 2018, 07:34
y(y − 3)(y + 2)(y − 1) = 0

=> Atleast one among y, (y-3), (y+2), (y-1) is zero

=> The value y is among (0, 3, -2, 1) (only 4 values are possible for y)

Statement 1

$$y^2 - 3y \neq 0$$

=> $$y(y-3) \neq 0$$

=> Y is neither 0 nor 3 => Y can be -2 or 1

y could be -2 in which case y is negative

y could be 1 in which case y is positive

Statement 1 is not sufficient

Statement 2

$$y^2 -3y + 2 \neq 0$$

only 4 values are possible for y and only 3, -2, 0 satisfy above equation

y could be -2 which is negative

y could be 0 or 3 => y is non negative

Statement 2 is insufficient

Combining statements 1 and 2

The only possible values of y is -2

Statements 1 and 2 together are sufficient

Hence option C
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If y(y − 3)(y + 2)(y − 1) = 0, is y negative? &nbs [#permalink] 29 Jul 2018, 07:34
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