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# If xy > 3x – xy, is y > 1? (1) y > 1.5 (2) x > 0

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Math Expert
Joined: 02 Sep 2009
Posts: 47918
If xy > 3x – xy, is y > 1? (1) y > 1.5 (2) x > 0  [#permalink]

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14 Mar 2017, 02:59
00:00

Difficulty:

55% (hard)

Question Stats:

48% (01:06) correct 52% (00:58) wrong based on 60 sessions

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If xy > 3x – xy, is y > 1?

(1) y > 1.5
(2) x > 0

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Senior Manager
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 433
Location: India
Re: If xy > 3x – xy, is y > 1? (1) y > 1.5 (2) x > 0  [#permalink]

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15 Mar 2017, 05:32
1
xy > 3x – xy
or x(2y-3)>0
therefore x>0 or y>1.5
or x<0 or y<1.5

St 1: y>1.5. therefor y>1. ANSWER
St 2: x>0. condition 1 applies. therefore y>1.5 or y>1. ANSWER

option D
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Senior Manager
Joined: 06 Dec 2016
Posts: 251
Re: If xy > 3x – xy, is y > 1? (1) y > 1.5 (2) x > 0  [#permalink]

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16 Mar 2017, 12:12
1) the question asked if is y > 1?, the statement says y > 1.5. No need to work out anything
1 is sufficient

2) 2 is also sufficient. If x is a number greater than 0, then y will always be 1.5

Director
Joined: 27 May 2012
Posts: 525
If xy > 3x – xy, is y > 1? (1) y > 1.5 (2) x > 0  [#permalink]

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16 Jul 2018, 04:11
Bunuel wrote:
If xy > 3x – xy, is y > 1?

(1) y > 1.5
(2) x > 0

Dear Moderator ,

Is this question , as it is supposed to be . The statement itself gives the answer.

Edit :

My Bad question is perfect. Did not realize that x<0 and y <1.5 can also be a solution .
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- Stne

Math Expert
Joined: 02 Aug 2009
Posts: 6521
Re: If xy > 3x – xy, is y > 1? (1) y > 1.5 (2) x > 0  [#permalink]

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16 Jul 2018, 06:02
If xy > 3x – xy, is y > 1?
$$xy>3x-xy........2xy>3x........2xy-3x>0.........x(2y-3)>0$$
so two case-
a) x>0, so $$2y-3>0.......2y>3.......y>\frac{3}{2}$$
b) x<0, so $$2y-3<0.......2y<3.......y<\frac{3}{2}$$

(1) y > 1.5
clearly y>1
sufficient

(2) x > 0
see case (a), if x>0, $$y>\frac{3}{2}$$
sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If xy > 3x – xy, is y > 1? (1) y > 1.5 (2) x > 0 &nbs [#permalink] 16 Jul 2018, 06:02
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