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If 2x > 3y, is x negative? [#permalink]
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23 May 2010, 00:35
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If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0
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If 2x > 3y, is x negative? [#permalink]
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23 May 2010, 02:49
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Re: is X negative [#permalink]
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23 May 2010, 09:54
Bunuel wrote: dimitri92 wrote: If 2x>3y , is X negative
1) y>0 2) 2x+5y20=0 Given: \(2x>3y\). Q: is \(x<0\)? (Note here that if \(y\) is any positive number than we would have \(2x>positive\), and in order that to be true \(x\) must be some negative number). (1) \(y>0\) > \(2x>3y>0\) > \(x<0\). Sufficient. (2) \(2x+5y20=0\) > \(2x=205y\) > \(20+5y>3y\) > \(y>10\). Same as above: \(x<0\). Sufficient. Answer: D. Can you please explain stmt. 2 again. Unable to understand the following stmt \(20+5y>3y\)
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Re: is X negative [#permalink]
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23 May 2010, 10:08
onedayill wrote: Bunuel wrote: dimitri92 wrote: If 2x>3y , is X negative
1) y>0 2) 2x+5y20=0 Given: \(2x>3y\). Q: is \(x<0\)? (Note here that if \(y\) is any positive number then we would have \(2x>positive\), and in order that to be true \(x\) must be some negative number). (1) \(y>0\) > \(2x>3y>0\) > \(x<0\). Sufficient. (2) \(2x+5y20=0\) > \(2x=205y\) > \(20+5y>3y\) > \(y>10\). Same as above: \(x<0\). Sufficient. Answer: D. Can you please explain stmt. 2 again. Unable to understand the following stmt \(20+5y>3y\) (2) \(2x+5y20=0\) > \(2x=205y\) > given \(2x>3y\), substitute \(2x\) > \((205y)>3y\) > \(20+5y>3y\) > \(y>10\) > \(y=positive\), as discussed above if \(y\) is any positive number then \(x\) must be some negative number: \(x<0\). Sufficient. Hope it's clear.
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Re: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 [#permalink]
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29 Jun 2013, 07:45
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fozzzy wrote: In statement 2 we can write the equation 2x+3y+2y = 20 we know 2x+3y is positive and we get y = 10 hence same as statement 1 is this approach correct? If 2x > 3y, is x negative?(1) y > 02x > +ve number, hence x is negative. Sufficient (2) 2x + 5y  20 = 0The area defined by 2x > 3y is the area under the red line. If we know that \(2x + 5y  20 = 0\) (blue line) (given the initial condition) we can say that x is negative because they intersect when x is negative. (refer to the image) Sufficient Your approach is correct. We know that 2x+3y is negative (typo I think), so \(2x + 3y +2y= 20\) can be seen as \(ve +2y=20\) so y is positive for sure as \(2y=20+(+ve)\)
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Re: If 2x > 3y, is x negative [#permalink]
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25 Aug 2013, 00:04
SUNGMAT710 wrote: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 2x > 3y 2x + 3y<0 (1) Statement 1If y>0 & 2x + 3y<0 Then x must be Negative. Sufficient Statement 22x + 5y  20 = 0 2x + 5y = 20 (2x + 3y) + 2y=20 We can write 2y + some negative no = 20 2y = 20 + some Positiveno y = 10 + some Positiveno/2 This mean that y>10 2x + 3y<0 2x< 3y x < 1.5 (Positive no) because y is positive Then x must be Negative. Sufficient Answer D
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Re: If 2x > 3y, is x negative [#permalink]
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25 Aug 2013, 00:06
SUNGMAT710 wrote: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 From F.S 1, we know that 2x>0. Thus, x<0. Sufficient. From F.S 2, we know that \(y = \frac{202x}{5}\) , replacing this value , \(2x>3*\frac{202x}{5} \to\)\(10x>606x \to 4x>60\). Again, x<0. D.
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Re: If 2x > 3y, is x negative? [#permalink]
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10 Jan 2016, 05:17
We are given 2x > 3y need to find if x is negative?
(1) y > 0 x has to be negative to ensure that 2x > 3y Suff
(2) 2x + 5y  20 = 0 substituting y = (202x)/5 gives x>15 Suff
Answer D



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Re: If 2x > 3y, is x negative? [#permalink]
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10 Jan 2016, 05:18
NoHalfMeasures wrote: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 Hi, 2x > 3y... (a)If y<0, x can be both +ive and ive.. (b)if y>0, x will have to be +ive as 3y is positive and 2x , to be positive, has to have x as ive.. now lets see the choices.. (1) y > 0 If y>0, x is ive as proved in (b) above... suff (2) 2x + 5y  20 = 0.. this can be written as 2x+3y + 2y 20=0.. now 2x+3y<0, so 2y>20... or y is +ive and therefore x is ive.... suff ans D
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Re: If 2x > 3y, is x negative? [#permalink]
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10 Jan 2016, 05:58
chetan2u wrote: NoHalfMeasures wrote: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 Hi, 2x > 3y... (a)If y<0, x can be both +ive and ive.. (b)if y>0, x will have to be +ive as 3y is positive and 2x , to be positive, has to have x as ive.. now lets see the choices.. (1) y > 0 If y>0, x is ive as proved in (b) above... suff (2) 2x + 5y  20 = 0.. this can be written as 2x+3y + 2y 20=0.. now 2x+3y<0, so 2y>20... or y is +ive and therefore x is ive.... suff ans D how can you say 2x+3y<0?



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Re: If 2x > 3y, is x negative? [#permalink]
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10 Jan 2016, 06:20
paidlukkha wrote: chetan2u wrote: NoHalfMeasures wrote: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 Hi, 2x > 3y... (a)If y<0, x can be both +ive and ive.. (b)if y>0, x will have to be +ive as 3y is positive and 2x , to be positive, has to have x as ive.. now lets see the choices.. (1) y > 0 If y>0, x is ive as proved in (b) above... suff (2) 2x + 5y  20 = 0.. this can be written as 2x+3y + 2y 20=0.. now 2x+3y<0, so 2y>20... or y is +ive and therefore x is ive.... suff ans D how can you say 2x+3y<0? Hi, 2x + 3y <0 comes from 2x>3y.. 2x>3y.. add 2x to both sides.. 2x2x>3y+2x.. 0>2x+3y... hope it helps
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If 2x > 3y, is x negative? [#permalink]
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10 Jan 2016, 06:29
Hi, 2x + 3y <0 comes from 2x>3y.. 2x>3y.. add 2x to both sides.. 2x2x>3y+2x.. 0>2x+3y... hope it helps[/quote] Aye, it does! Thanks Also, if I understand, <> sign changes in multiplication only! Btw, St2 gives me x as +ve What am I doing wrong? (2) 2x + 5y  20 = 0 substituting y = (202x)/5 gives x>15 Suff



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Re: If 2x > 3y, is x negative? [#permalink]
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10 Jan 2016, 06:32
paidlukkha wrote: Hi, 2x + 3y <0 comes from 2x>3y.. 2x>3y.. add 2x to both sides.. 2x2x>3y+2x.. 0>2x+3y... hope it helps Aye, it does! Thanks Also, if I understand, <> sign changes in multiplication only![/quote] hi, yes you are right , whenever you multiply two sides on either side of equality with a ive sign or ive quantity, you are required to change the greater/lesser than sign.. 2x>3y.. 2x<3y..
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If 2x > 3y, is x negative? [#permalink]
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13 Jan 2016, 07:02
If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0
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If 2x > 3y, is x negative? [#permalink]
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13 Jan 2016, 07:42
Sash143 wrote: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 Given that 2x > 3 y> x<1.5 y and the question asks whether x<0. Per statement 1, y>0 > from this statement and the fact that x<1.5y, clearly we can see that x must be <0. Sufficient. Per statement 2, 2x + 5y  20 = 0 > y = (202x)/5 and from the given fact, y<2x/3 > x < 15. Again sufficient to answer the question asked. Hence both statements are sufficient to answer the question asked. D is thus the correct answer. Hope this helps.
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If 2x > 3y, is x negative? [#permalink]
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13 Jan 2016, 07:59
Sash143 wrote: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 It is clear that if x negative, 2x > 0, so we will wish to see whether 3y >0, if so 2x > 3y > 0. (1) y >0 => clearly, 2x > 3y > 0 => x negative (2) 2x + 5y  20 = 0. => 2x + 5y =20 Because 2x > 3y => 2x < 3y => 2x + 5y < 3y + 5y =2y or 20 < 2y => 10<y => 2x > 3y > 30 => x negative So, answer is D



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Re: If 2x > 3y, is x negative? [#permalink]
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13 Jan 2016, 08:32



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Re: If 2x > 3y, is x negative? [#permalink]
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13 Jan 2016, 08:50
Bunuel wrote: Sash143 wrote: If 2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y  20 = 0 Please search before posting. Thank you. Bunuel I did search before posting but couldn't find one! Anyway my bad
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Re: If 2x > 3y, is x negative? [#permalink]
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13 Jan 2016, 09:29
Bunuel wrote: If 2x>3y , is x negative
Given: \(2x>3y\). Question: is \(x<0\)? (Note here that if \(y\) is any positive number then we would have \(2x>positive\), and in order that to be true \(x\) must be some negative number).
(1) \(y>0\) > \(2x>3y>0\) > \(x<0\). Sufficient.
(2) \(2x+5y20=0\) > \(2x=205y\) > \(20+5y>3y\) > \(y>10\). The same as above: \(x<0\). Sufficient.
Answer: D. we have 2 equation and two variables so we can calculate . so answer is D.




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