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# If x and y are integers and x + y = 21, is x > 19? (1) 2y > 19 + y

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If x and y are integers and x + y = 21, is x > 19? (1) 2y > 19 + y  [#permalink]

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14 Mar 2017, 01:20
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Difficulty:

55% (hard)

Question Stats:

70% (01:47) correct 30% (02:23) wrong based on 30 sessions

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If x and y are integers and x + y = 21, is x > 19?

(1) 2y > 19 + y
(2) 3x/y > 51x

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Re: If x and y are integers and x + y = 21, is x > 19? (1) 2y > 19 + y  [#permalink]

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15 Mar 2017, 04:53
x +y = 21

St 1: 2y>19+y or y>19. hence x<2. therefore xis not >19 . ANSWER

St 2: 3x/y >51x
or x/y>17x
or x(1-17y)/y>0
therefore x>0, 0<y<1/17. for this x>19

or x<0 , y<0 or y>1/17. for this we cannot say. INSUFFICIENT

Option A
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Re: If x and y are integers and x + y = 21, is x > 19? (1) 2y > 19 + y  [#permalink]

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13 Dec 2017, 07:24
Bunuel wrote:
If x and y are integers and x + y = 21, is x > 19?

(1) 2y > 19 + y
(2) 3x/y > 51x

Hi Bunuel,

Are you sure that answer is A? How do you prove that Statement 2 is insufficient?

2) 3x/y > 51x............x/y>17x

If y>0.... then x>17xy.....x-17xy>0....x(1-17y)>0

As y is positive... (1-17y) is negative........x must be negative in order to have x(1-17y)>0

x is NOT greater than 19

If y 51x
x/y > 17x

In the resulting inequality, x can be positive only if y is also positive.
There is ONLY ONE SOLUTION for x+y = 21 such that x>19 and x and y are both positive:
x=20, y=1.
If this solution does not satisfy x/y > 17x, then it is not possible that x>19.
Plugging x=20 and y=1 into x/y > 17x, we get:
20/1 > 17*20
20 > 340.
Doesn't work.
Thus, it is not possible that x>19, implying that the answer to the question stem is NO.
SUFFICIENT.

Thanks

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: If x and y are integers and x + y = 21, is x > 19? (1) 2y > 19 + y &nbs [#permalink] 13 Dec 2017, 07:24
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