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# If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0

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Math Expert
Joined: 02 Sep 2009
Posts: 44655
If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0 [#permalink]

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21 Apr 2017, 07:55
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Difficulty:

75% (hard)

Question Stats:

49% (01:46) correct 51% (01:31) wrong based on 116 sessions

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If -3x > 4y, is x < 0?

(1) y > 0

(2) 3x + 5y – 20 = 0
[Reveal] Spoiler: OA

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Manager
Joined: 25 Apr 2016
Posts: 53
Re: If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0 [#permalink]

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21 Apr 2017, 08:03
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given 3x+4y<0
statement 1st: provided y> 0, x has to be negative to satisfy the question stem => sufficient
statement 2nd : 3x +5y =20 but 3x+4y <0 => y>0 => x<0 => sufficient
option-D
Director
Joined: 21 Mar 2016
Posts: 544
Re: If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0 [#permalink]

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21 Apr 2017, 08:49
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attari92 wrote:
given 3x+4y<0
statement 1st: provided y> 0, x has to be negative to satisfy the question stem => sufficient
statement 2nd : 3x +5y =20 but 3x+4y <0 => y>0 => x<0 => sufficient
option-D

hi can u explain ur statement 2
Manager
Joined: 04 Apr 2015
Posts: 106
Re: If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0 [#permalink]

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22 Apr 2017, 00:37
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attari92 wrote:
given 3x+4y<0
statement 1st: provided y> 0, x has to be negative to satisfy the question stem => sufficient
statement 2nd : 3x +5y =20 but 3x+4y <0 => y>0 => x<0 => sufficient
option-D

IMO A

since we dont know the sign of y in statement 2 so we can say anything about answer being D
Manager
Joined: 25 Apr 2016
Posts: 53
Re: If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0 [#permalink]

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22 Apr 2017, 07:15
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varundixitmro2512 wrote:
attari92 wrote:
given 3x+4y<0
statement 1st: provided y> 0, x has to be negative to satisfy the question stem => sufficient
statement 2nd : 3x +5y =20 but 3x+4y <0 => y>0 => x<0 => sufficient
option-D

IMO A

since we dont know the sign of y in statement 2 so we can say anything about answer being D

look, it's been mentioned in the question stem that 3x+4y<0 but how come 3x + 4y +y =20 ? It means that the negative part (3x+4y) ought to be added with a positive 'y' in order to make the expression equals 20 , you see
Intern
Joined: 19 Sep 2016
Posts: 35
If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0 [#permalink]

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10 Sep 2017, 10:32
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A. -3x>4y - statement 1 - y>0, means -3x>a where a is 4y which is a positive value and for -3x to be greater than the positive value x shall be < 0. Hence sufficient.
Statement 2 - 3x+5y=20 which is also an equation of a decreasing line as the slope is negative and the values for the (x,y) pair can be (-10,10), (-5,7), (0,4), (5,1), (10,-2) where can be negative or less than zero but it can also be positive but for all positive values of x the equation -3x>4y will not be satisfied hence x can only be <0. Hence statement 2 is sufficient. So answer is D

sorry missed an important point there so updated the response. correct answer is D.

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Intern
Joined: 27 Apr 2015
Posts: 40
GMAT 1: 370 Q29 V13
If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0 [#permalink]

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30 Dec 2017, 10:23
Bunuel wrote:
If -3x > 4y, is x < 0?

(1) y > 0

(2) 3x + 5y – 20 = 0

Given -3x>4y

Find is x<0 i.e is 'x'-ve

Now -3x > 4y
=> OR 3x < -4y
=> OR x < $$\frac{-4}{3}$$*y ---(1)
=> Therefore from (1) x<0 FOR SURE if y>0

Statement 1 y>0
=> Since y>0, Therefore x<0 SUFFICIENT

Statement 2 3x+5y-20=0
=> 3x+5y=20 ------------- (2)
=> Given 3x<-4y
=> OR 3x+4y<0
=> OR 3x+4y+y<0+y
=> OR 3x+5y<y
=> OR 20<y ------- from (2)
=> OR y>20
=> Since y>20 i.e y>0
=> Therefore 'x' is -ve i.e x<0
=> SUFFICIENT

Therefore 'D'

Thanks
Dinesh
If -3x > 4y, is x < 0? (1) y > 0 (2) 3x + 5y – 20 = 0   [#permalink] 30 Dec 2017, 10:23
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