|y - 1/2| < 11/2

Hi boomgoesthegmat,

This question asks us to solve for what COULD be the value of the one variable in the prompt. Since the answer choices are numbers, we can BRUTE FORCE a solution relatively easy - just plug in the answers until you find the one that 'fits' the inequality.

We're looking for a value that is LESS than 11/2 (or 5.5):

Answer A: -11
|-11 - 1/2| = |-11.5| = 11.5
NOT less than 5.5

Answer B: -11/2
|-11/2 - 1/2| = |-12/2| = 6
NOT less than 5.5

Answer C: 11/2
|11/2 - 1/2| = |10/2| = 5
This IS less than 5.5, so this MUST be the answer.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

boomgoesthegmat wrote:If |y - 1/2| < 11/2, which of the following could be a value of y?

A) -11
B) -11/2
C) 11/2
D) 11
E) 22

---------ASIDE-----------------------------------------------

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

----NOW ONTO THE QUESTION!!!!-------------------

GIVEN: |y - 1/2| < 11/2
Apply Rule #1 to get: -11/2 < y - 1/2 < 11/2
Multiply all parts by 2 to get: -11 < 2y - 1 < 11
Add 1 to all parts to get: -10 < 2y < 12
Divide all parts by 2 to get: -5 < y < 6

If y is BETWEEN -5 and 6, then the correct answer is C

Cheers,
Brent