SOLUTION

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

\(|y-\frac{1}{2}| < \frac{11}{2}\), is equivalent to \(-\frac{11}{2}<y-\frac{1}{2}< \frac{11}{2}\).

Add \(\frac{1}{2}\) to each part of the inequality: \(-\frac{11}{2}+\frac{1}{2}<y< \frac{11}{2}+\frac{1}{2}\) --> \(-5<y<6\). Only answer C is from this range.

Answer: C.
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An Easy way for this type of Problem is as follows

When ever you see an in equality with modulus remember these two formulas
1.) |x-b| < c .................This always means that ............ -c+b < x < c +b
2.) |x-b| > c ................. This always means that .......... Either x < -c+b .................... or x > c+b

Use this here and see.

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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It seems that you need to brush up fundamentals on absolute value.

Theory: math-absolute-value-modulus-86462.html

PS questions on Absolute Values: search.php?search_id=tag&tag_id=58
DS questions on Absolute Values: search.php?search_id=tag&tag_id=37

Tough inequality and absolute value questions: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.
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If |y-1/2| < 11/2

First calculate origin (y-1/2)=0. Origin is +1/2.

This should be read as distance from origin 1/2 is less than 11/2 units. So there is range here.

So, on the right side of 1/2 we add 11/2 units and on the left side we minus 11/2 units

(1/2-11/2= -5)---------------------(1/2)---------------------(1/2+11/2 = 6)

So our answer must be in range of -5 to 6. -5<y<6

only 11/2 lies in this range. Hence answer.

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



This means, -5 < y < 6

Therefore, Option C is the correct answer.
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well, here are 2 methods -

lets just check answers,beginning with ans C

|11/2- (1/2)| <11/2 yes,of course, since u subtract from the number 11/2 some portion.


method 2-

|y-1/2| < 11/2

if y>1/2, then y-1/2 < 11/2 y<6 , so ,we need some number between 1/2 and 6

if y<1/2, then 1/2- y<11/2 , y>6 reject it,since it contradicts with y<1/2

so, now lets check all answer choices and find the answer between 1/2 and 6

btw, do u post 700+ OG13 questions? havent seen them.
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SOLUTION

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

\(|y-\frac{1}{2}| < \frac{11}{2}\), is equivalent to \(-\frac{11}{2}<y-\frac{1}{2}< \frac{11}{2}\).

Add \(\frac{1}{2}\) to each part of the inequality: \(-\frac{11}{2}+\frac{1}{2}<y< \frac{11}{2}+\frac{1}{2}\) --> \(-5<y<6\). Only answer C is from this range.

Answer: C.
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The inequality becomes:
-11/2 < y-1/2 < +11/2

Hence, 1/2 has to be added to each inequality:
-11/2 + 1/2 = -5
11/2 + 1/2 = 6

After simplifying, we get:
-5< y < 6
The only option that lies between -5 and 6 is 11/2, which when simplified is 5.5

Thus, the answer has to be C.

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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Given: \(|y-\frac{1}{2}| < \frac{11}{2}\)

Asked: Which of the following could be a value of y?

\(|y-\frac{1}{2}| < \frac{11}{2}\)
\(-\frac{11}{2}<y-\frac{1}{2}<\frac{11}{2}\)
\(-\frac{11}{2}+\frac{1}{2}<y<\frac{11}{2}+\frac{1}{2}\)
\(-5<y<6\)

Since 11/2 = 5.5 lies within the range \(-5<y<6\)

IMO C
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If y<1/2, then 1/2-y<11/2 ie 1/2-11/2 <y, ie -5<y. so y lies between -5<y<1/2.

Am I correct???

SOURH7WK, yep, u r correct. it is a typo.forgive me all my sins, or only poor computing skills ))
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We have to see how far the value of y is on the number line
so basically, what we have here is

The distance of y from 1/2 is< 5.5
so it could be from 5 to 6.

hence answer is C

Why is

|y-1/2| < 11/2 equivalent to -11/2 < |y-1/2| < 11/2

Why am I not seeing this and why didn´t I come up with it?

Thanks Bunnel for such a valuable reply..and +1 for you as well

I was wondering, if the equation stands at -5<y<6, should not it be that both B & C are right..
Thanks

-11/2=-5.5<-5 and we know that -5<y, thus y cannot be -5.5.

Hope it's clear.
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Ans:

the first case gives us y<6 and the second case gives –(y-1/2)<11/2 so y >-5 only option c falls in the range of -5<y<6 answer (C).

\(|y-\frac{1}{2}| < \frac{11}{2}\) <--- basically what this is saying is, "we start at 0.5, and we CANNOT go 5.5 or more steps in either direction"

which means -5 < x < 6

the only one of the options that fit the restriction is 11/2 = 5.5 ... So answer (C)