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# If all members of Set X are positive integers, what is the

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GMAT Instructor
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If all members of Set X are positive integers, what is the [#permalink]

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09 Jul 2006, 04:29
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If all members of Set X are positive integers, what is the range of Set X?

(1) The positive difference between the square of the largest number in Set X and the square of the smallest number in Set X is 99.
(2) The sum of the largest number in Set X and the smallest number in Set X is not 11.

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SVP
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09 Jul 2006, 06:00
pretty tough calculations but got E.
got three pairs (1-11, 15-18, 49-59) that work for i and ii.
want to know the best approach..

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09 Jul 2006, 06:32
stmt 1, I get 2 pairs (10,1) (18,15) -- insuff

stmt 2, can be anything

combining I get (18,15)--C

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09 Jul 2006, 06:53
HIMALAYA wrote:
pretty tough calculations but got E.
got three pairs (1-11, 15-18, 49-59) that work for i and ii.
want to know the best approach..

small update on typo:

pairs = 1-11, 15-18, 49-50

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Director
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09 Jul 2006, 07:36
thats E then. Himalaya I dont think 11 and 1 will give you 99. 121-1=120

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09 Jul 2006, 08:07
shahnandan wrote:
thats E then. Himalaya I dont think 11 and 1 will give you 99. 121-1=120

one more typo.
thats 10 and 1.
thanks.

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09 Jul 2006, 13:42
If y is the largest and x is the smallest,

y^2-x^2=99

But 99=99*1=33*3=11*9

So (y+x,y-x) could be (99,1), (33,3) or (11,9)

Thus (y,x) could be (50,49),(18,15), or (10,1)

Range could be 1,3,or 9

So (1) is not sufficient

(2) is not sufficent by itself

(1) and (2) together - range could be 3 or 9 (Not Sufficient)

OA - E

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09 Jul 2006, 13:42
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