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|y - 1/2| < 11/2

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by Matt@VeritasPrep » Thu Apr 28, 2016 2:13 pm
If y is positive, we'd have

y - 1/2 < 11/2

y < 11/2 + 1/2

y < 6

So our solution set is

0 < y < 6

11/2 => 5.5 falls in that range, so C works.
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by [email protected] » Thu Apr 28, 2016 6:46 pm
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

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Rich
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by Jeff@TargetTestPrep » Tue Mar 20, 2018 4:11 pm
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

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by Brent@GMATPrepNow » Tue Mar 20, 2018 4:20 pm
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
Brent Hanneson - Creator of GMATPrepNow.com
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