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!!
If x is a positive integer, is x^1/2 < 2.5x - 5
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There's a problem with squaring both sides if one of the sides can possibly be a negative number (before being squared)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!!
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
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Do we need to consider both positive and negative values of square root or only the positive value ?