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

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Re: If |y-1/2| < 11/2, which of the following could be a value [#permalink]

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New post 08 May 2015, 05:56
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Here's a visual solution for this question:

\(|y-\frac{1}{2}|\) represents the distance of y from the point \(\frac{1}{2}\) = 0.5 on the number line.

The given inequality tells us that the distance of y from the point 0.5 is less than \(\frac{11}{2}\) (that is, 5.5)

The points that are at a distance of 5.5 from 0.5 on the number line are: -5 and 6

Image

This means, -5 < y < 6

Therefore, Option C is the correct answer.
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Re: If |y-1/2| < 11/2, which of the following could be a value [#permalink]

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New post 11 Apr 2016, 16:35
If you are confused by the algebraic solution, then it might be easier to plug in when absolute values are involved.
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Re: If |y-1/2| < 11/2, which of the following could be a value [#permalink]

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Bunuel wrote:
If \(|y-\frac{1}{2}| < \frac{11}{2}\), which of the following could be a value of y?

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



Solution:

We must solve the inequality for two cases:

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

|y – ½| < 11/2

y – ½ < 11/2

Add ½ to both sides of the equation:

y < 6

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

|y – ½| < 11/2

-(y – ½) < 11/2

-y + ½ < 11/2

Subtract ½ 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 this criterion is answer choice C, 11/2.

Answer: C
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Re: If |y-1/2| < 11/2, which of the following could be a value [#permalink]

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Re: If |y-1/2| < 11/2, which of the following could be a value [#permalink]

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New post 30 Aug 2017, 07:48
Bunuel shashankism Engr2012

Hi Experts, how much I try I can not refrain from opening the modulus and
assigning +ve and -ve values to expressions inside modulus. Is there any
short cut approach to this , please see screenshot.
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If |y-1/2| < 11/2, which of the following could be a value [#permalink]

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New post 31 Aug 2017, 09:05
hi EgmatQuantExpert

Can you please explain the steps in your post more elaborately?
I am able to understand |x| < a means -a < x < a
but falter when taking complex inequalities like |x-a| < b

WR,
Arpit
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If |y-1/2| < 11/2, which of the following could be a value   [#permalink] 31 Aug 2017, 09:05

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