If x is an integer and |2x + 3| ≤ 12 then which of the following must

Question

If x is an integer and |2x+3|≤12 , then which of the following must be true? A. x < -9 B. x < -8 C. x > -8 D. x < 4 E. x > 4

GMATinsight · Accepted Answer

|2x+3|≤12 i.e. -12 ≤ 2x+3 ≤ 12 i.e. -12-3 ≤ 2x ≤ 12-3 i.e. -15 ≤ 2x ≤ 9 i.e. -7.5 ≤ x ≤ 4.5 Out of all options we see A. x < -9 Is INCORRECT as all values of x are greater than -9 B. x < -8 Is INCORRECT as all values of x are greater than -8 C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8 D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4 E. x > 4 Is INCORRECT as x may be less than 4 as well Answer: Option C

saurabh9gupta · Answer

use this link to solve - https://gmatclub.com/forum/inequalities ... 06653.html

KarishmaB · Answer

|2x+3|≤12

|x+3/2|≤6

So x is a point that is a distance of 6 or less from -1.5
So x would be less than 4.5 or more than -7.5

-7.5 \leq x \leq 4.5

<------------------------  (-7.5) ================== (4.5)  ---------------------->

x can take any value in the "===" region. For each value in this region, x is definitely greater than -8.

Answer (C)

HAPPYatHARVARD · Answer

Hi   VeritasKarishma Another way!

fogarasm · Answer

Quick clarification question - with regard to answer D, x is an integer—so 4.25 being greater than 4 is not the reason why the choice is wrong. It's because x could be 4, which is not included by x < 4. Is that correct?

GMATinsight · Answer

fogarasm Thank you for pointing out the mistake in the mistake. I missed the information in quick solving the question.

GMATBusters · Answer

Graphical approach shall be as per attached sketch WhatsApp Image 2018-10-21 at 10.32.28.jpeg

KarishmaB · Answer

Yes, this method uses the definition of absolute values. The method I have shown is based on the concept of looking at absolute value in terms of distance.

shobhiitgupta · Answer

I got the same range but won't x > -8 include values above 4.5 ?

GMATinsight · Answer

The logic is, When it's known that -7.5 ≤ x ≤ 4.5 then for all possible values of x we can say that each value will certainly be greater than -8 on the other hand you can prove all other options incorrect as per the following explanation (already mentioned in previous solutions) A. x < -9 Is INCORRECT as all values of x are greater than -9 B. x < -8 Is INCORRECT as all values of x are greater than -8 C. x > -8 Is CORRECT because all values of x in the calculated range of values of x are greater than -8 D. x < 4 Is INCORRECT because x may be 4 which is NOT less than 4 E. x > 4 Is INCORRECT as x may be less than 4 as well I hope this helps!!!

Kinshook · Answer

If x is an integer and |2x+3|≤12 , then which of the following must be true? -12 <= 2x+3 <= 12 -7.5 <= x <= 4.5 A. x < -9 B. x < -8 C. x > -8: MUST BE TRUE D. x < 4 E. x > 4 IMO C Posted from my mobile device

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If x is an integer and |2x + 3| ≤ 12 then which of the following must

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GMAT Problem Solving (PS) Questions

If x is an integer and |2x + 3| ≤ 12 then which of the following must

Prep Toolkit

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