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If x is a positive integer, is x^1/2 < 2.5x - 5

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If x is a positive integer, is x^1/2 < 2.5x - 5

by ogbeni » Mon Sep 21, 2009 3:21 pm
If x is a positive integer, is x^1/2 < 2.5x - 5 ?

1. x < 3
2. x is a prime number


OA is A, I went for C

Here's how I approached the problem.

I didn't like the square root on the LHS so I restated the question as "Is x< (2.5x - 5)^2". Is there anything wrong with my operation to square both sides of the inequality?

Considering the statements:
[spoiler]STMT 2: Considering prime number (2), I get "Is 2<0" - NO. Considering prime number (3), I get "Is 3<6.25" - YES; therefore, 2 is INSUFFICIENT - ELIMINATE B

STMT 1: The values of x are 1 and 2. Considering (1), I get "Is 1<6.25" - YES. Considering (2) from above, the answer is NO, therefore 1 is INSUFFICIENT - ELIMINATE A

Combining both statements, we are left with only prime number (2), therefore we have a NO, hence C is SUFFICIENT.[/spoiler] Alas I'm wrong :(

Someone please provide some illumination!!
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Re: If x is a positive integer, is x^1/2 < 2.5x - 5

by Brent@GMATPrepNow » Mon Sep 21, 2009 5:15 pm
ogbeni wrote:If x is a positive integer, is x^1/2 < 2.5x - 5 ?

1. x < 3
2. x is a prime number


OA is A, I went for C

Here's how I approached the problem.

I didn't like the square root on the LHS so I restated the question as "Is x< (2.5x - 5)^2". Is there anything wrong with my operation to square both sides of the inequality?

Considering the statements:
[spoiler]STMT 2: Considering prime number (2), I get "Is 2<0" - NO. Considering prime number (3), I get "Is 3<6.25" - YES; therefore, 2 is INSUFFICIENT - ELIMINATE B

STMT 1: The values of x are 1 and 2. Considering (1), I get "Is 1<6.25" - YES. Considering (2) from above, the answer is NO, therefore 1 is INSUFFICIENT - ELIMINATE A

Combining both statements, we are left with only prime number (2), therefore we have a NO, hence C is SUFFICIENT.[/spoiler] Alas I'm wrong :(

Someone please provide some illumination!!
There's a problem with squaring both sides if one of the sides can possibly be a negative number (before being squared)
e.g., 2 is greater than -3, but 2^2 is not greater than (-3)^2.

So, for the calculations in statement (1), if you plug in x=1 you get (1)^1/2 IS NOT less than 2.5(1) - 5.
However, if you square both sides first, we get 1 IS less than 6.25
Brent Hanneson - Creator of GMATPrepNow.com
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by ogbeni » Mon Sep 21, 2009 5:27 pm
Brent,

Again thanks for the illumination. Sometimes working under time constraints makes you not think in a wholesome manner :(

Lesson learned.
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by maximus123 » Wed Sep 23, 2009 12:17 am
Do we need to consider both positive and negative values of square root or only the positive value ?
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