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another tricky question

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another tricky question

by sana.noor » Sat Dec 29, 2012 11:18 pm
If n is a positive integer, is n equal to 100 ?

(1) n^(1/2) > 9
(2) n^(1/2) < 11
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by Param800 » Sun Dec 30, 2012 5:54 am
(1) N^(1/2) > 9 , it can have any value of n ie from 100, 102, 103....infinity..

So, insufficient

(2) N^(1/2) < 11 , it can also get any value ie from 100, 90,...anything whose square root is less than 11.

So, insufficient

When we combine them--

N^(1/2) should be between 9 and 11. So, one number which satisfies it is N= 10, but be careful, there re some other numbers which could satisfy this inequality like 99,97,98...etc

So, this is also insufficient.
Thus, answer is E
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by sana.noor » Sun Dec 30, 2012 6:17 am
so according to question, n is integer but square root of n could be a non-integer?? am i right??
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by Param800 » Sun Dec 30, 2012 6:24 am
Yes, N is n integer, it's square root can be integer or a non integer. See this example-

N= 100 , Square root = 10
N= 98 , Square root= non integer
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by Brent@GMATPrepNow » Mon Dec 31, 2012 8:49 am
sana.noor wrote:If n is a positive integer, is n equal to 100 ?

(1) n^(1/2) > 9
(2) n^(1/2) < 11
Target question: Does n = 100?

Aside: x^(1/2) is the same as sqrt(x)

Statement 1: n^(1/2) > 9
In other words, sqrt(n) > 9
Square both sides of the inequality to get: n > 81
There are several integer values of n that meet this condition. Here are two:
Case a: n = 99, in which case n does not equal 100
Case b: n = 100, in which case n does equal 100
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n^(1/2) < 11
In other words, sqrt(n) < 11
Square both sides of the inequality to get: n < 121
There are several integer values of n that meet this condition. Here are two:
Case a: n = 99, in which case n does not equal 100
Case b: n = 100, in which case n does equal 100
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We know that 9 < sqrt(n) < 11
In other words, 81 < n < 121
There are still several integer values of n that meet this condition. Here are two:
Case a: n = 99, in which case n does equal 100
Case b: n = 100, in which case n does equal 100
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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