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# Is x greater than 2? (You may assume y is not equal to zero.)

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Math Expert
Joined: 02 Sep 2009
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Is x greater than 2? (You may assume y is not equal to zero.)  [#permalink]

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22 Oct 2017, 05:50
00:00

Difficulty:

45% (medium)

Question Stats:

55% (01:51) correct 45% (01:23) wrong based on 56 sessions

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Is x greater than 2? (You may assume y is not equal to zero.)

(1) x/y is greater than 2.
(2) 1/y is less than 1.

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Is x greater than 2? (You may assume y is not equal to zero.)  [#permalink]

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22 Oct 2017, 08:00
(1) x/y >2 => x>2y, Since we don’t know whether y is integer & >0 , So cannot come to a conclusion. INSUFFICIENT

(2) 1/y<1 => y>1, We don’t know the value of x. Irrelevant . INSUFFICIENT.

Adding (1) + (2) , we get x>2 . SUFFICIENT.

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Re: Is x greater than 2? (You may assume y is not equal to zero.)  [#permalink]

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22 Oct 2017, 08:35
Bunuel wrote:
Is x greater than 2? (You may assume y is not equal to zero.)

(1) x/y is greater than 2.
(2) 1/y is less than 1.

Statement 1: $$\frac{x}{y}>2$$, this implies if $$y<0$$, then $$x<0$$ and if $$0<y<1$$ then $$x<2$$ so we have a No for our question stem

but if $$y>1$$, then $$x>2$$, so we will have a Yes for our question stem. Hence insufficient

Statement 2: this implies that either $$y<0$$ or $$y>1$$ but nothing mentioned about $$x$$. Insufficient

Combining 1 & 2 we don't know whether $$y$$ is positive or negative. if $$y$$ is positive then $$x>2$$ but if $$y$$ is negative then $$x<2$$. Hence insufficient

Option E
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Re: Is x greater than 2? (You may assume y is not equal to zero.)  [#permalink]

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23 Oct 2017, 14:45
Bunuel wrote:
Is x greater than 2? (You may assume y is not equal to zero.)

(1) x/y is greater than 2.
(2) 1/y is less than 1.

(1) x/y >2 => It can be possible by number of values for x and y. so statement 1 does not give sufficient answer. So cannot come to a conclusion. INSUFFICIENT.

(2) 1/y<1 => It does not give any information about value of X. Irrelevant . INSUFFICIENT.

Adding (1) + (2) , now Y is greater than 1, so X should be greater than 2 if X/Y >2 we get x>2 . SUFFICIENT.

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Re: Is x greater than 2? (You may assume y is not equal to zero.)  [#permalink]

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23 Oct 2017, 20:52
Bunuel wrote:
Is x greater than 2? (You may assume y is not equal to zero.)

(1) x/y is greater than 2.
(2) 1/y is less than 1.

(1) x/y >2 => It can be possible by number of values for x and y. so statement 1 does not give sufficient answer. So cannot come to a conclusion. INSUFFICIENT.

(2) 1/y<1 => It does not give any information about value of X. Irrelevant . INSUFFICIENT.

Adding (1) + (2) , now Y is greater than 1, so X should be greater than 2 if X/Y >2 we get x>2 . SUFFICIENT.

in your solution, you have assumed that $$y>0$$ but the question doesn't mention that neither any of the statements

so if $$y=-1$$, then $$\frac{1}{y}=-1<1$$ and $$\frac{x}{y}>2$$ will imply that $$x<-2$$. Hence we have a NO for our question stem

but if $$y=2$$, then $$\frac{1}{y}=0.5<1$$ and $$\frac{x}{y}>2$$ will imply $$x>4$$. so we have a YES for our question stem.

Hence IMO answer should be E
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Re: Is x greater than 2? (You may assume y is not equal to zero.)  [#permalink]

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23 Oct 2017, 21:15
niks18 wrote:
Bunuel wrote:
Is x greater than 2? (You may assume y is not equal to zero.)

(1) x/y is greater than 2.
(2) 1/y is less than 1.

(1) x/y >2 => It can be possible by number of values for x and y. so statement 1 does not give sufficient answer. So cannot come to a conclusion. INSUFFICIENT.

(2) 1/y<1 => It does not give any information about value of X. Irrelevant . INSUFFICIENT.

Adding (1) + (2) , now Y is greater than 1, so X should be greater than 2 if X/Y >2 we get x>2 . SUFFICIENT.

in your solution, you have assumed that $$y>0$$ but the question doesn't mention that neither any of the statements

so if $$y=-1$$, then $$\frac{1}{y}=-1<1$$ and $$\frac{x}{y}>2$$ will imply that $$x<-2$$. Hence we have a NO for our question stem

but if $$y=2$$, then $$\frac{1}{y}=0.5<1$$ and $$\frac{x}{y}>2$$ will imply $$x>4$$. so we have a YES for our question stem.

Hence IMO answer should be E

niks18

You are right. Should be E. Silly Mistake.
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Re: Is x greater than 2? (You may assume y is not equal to zero.)  [#permalink]

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25 Oct 2017, 09:37
Bunuel wrote:
Is x greater than 2? (You may assume y is not equal to zero.)

(1) x/y is greater than 2.
(2) 1/y is less than 1.

From statement 1 we can deduce that x>2Y ; But we are no sure about value of Y so insufficient.

From Statement 2 we can deduce that y>1;But we are not sure about the value of x

so using both statement we can find the answer for the values of X

Re: Is x greater than 2? (You may assume y is not equal to zero.) &nbs [#permalink] 25 Oct 2017, 09:37
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