Problem Solving

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

We must solve the inequality for two cases:

Case 1: (y-1/2) is positive:

|y - 1/2| < 11/2

y - 1/2< 11/2

Add ½ to both sides of the equation:

y < 6

Case 2: (y-1/2) is negative:

|y - 1/2| < 11/2

-(y - 1/2) < 11/2

-y + 1/2 < 11/2

Subtract 1/2 from both sides of the equation:

-y < 5

y > -5

So we know that y is greater than -5 and less than 6. The only answer choice that fits these criteria is answer choice C, 11/2.

Answer: C

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