If |x - 3/4|

Question

If  |x - \frac{3}{4}| < \frac{9}{4} , which of the following could be a value of x?

A. -3
B. -2
C. 2
D. 3
E. 6

eakabuah · Answer

We are to find possible values of x that satisfy |x-3/4|<9/4
|x-3/4|<9/4 can be rewritten as -9/4<(x-3/4)<9/4
-9/4+3/4<x<9/4+3/4
-3/2<x<3
This means that x>-3/2 and x<3.

From the answer options only option C, x=2 satisfy this condition.
The answer is therefore C.

Posted from my mobile device

Mohammadmo · Answer

X- 3/4<9/4 ==》x<12/4 
-X+3/4< 9/4==》x>-6/4
Just option C can be in the range of x; -1.5<x<3

Posted from my mobile device

firas92 · Answer

\frac{-9}{4}<x-\frac{3}{4}<\frac{9}{4}

\frac{-6}{4}<x<\frac{12}{4}

-1.5<x<3

Out of all the answer choices, only 2 is within this range

Answer is  (C)

CrackverbalGMAT · Answer

In a question like this on Absolute values, instead of using the definition of |x-a|, using the distance approach will help you solve the question much faster.
Remember that |x-a| is the distance of the number x from the number a, on the number line.

So, essentially, this question is telling us that the distance of x from ¾ should be less than 9/4.
Let’s plot a number line and identify the critical points:

Attachment:

13th Aug 2019 - Reply 4.JPG [ 16.99 KiB | Viewed 6251 times ]

The 3 critical points in this situation are:

¾

¾ + \(\frac{9}{4}\) = 3

¾ - \(\frac{9}{4}\) = - 1.5

When we plot these points on the number line, it’s easy to figure out that x has to be between -1.5 and 3 if its distance from ¾ has to be less than \(\frac{9}{4}\).

From this, options A, B and E can be eliminated quite easily. However, option D can be eliminated because of the fact that the distance has to be LESS THAN \(\frac{9}{4}\) and not equal to \(\frac{9}{4}\); hence, x cannot be equal to 3, it has to be LESS THAN 3.

The correct answer option, therefore, is C.

Hope this helps!

Bunuel · Answer

Video Explanation

F0PDA1jXVmE

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If |x - 3/4| < 9/4, which of the following could be a value of x?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions