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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Which of the following inequalities holds if 3.24<x<5. tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Which of the following inequalities holds if 3.24<x<5. [GMAT math practice question] Which of the following inequalities holds if 3.24 A. |x+4.3|<1.06 B. |x-4.3|<1.06 C. |x-2.1|<0.53 D. |x+2.1|<0.53 E. |x-2.1|<1.06 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Quote:
[GMAT math practice question]

Which of the following inequalities holds if 3.24
A. |x+4.3|<1.06
B. |x-4.3|<1.06
C. |x-2.1|<0.53
D. |x+2.1|<0.53
E. |x-2.1|<1.06
Hi Max@Math Revolution,
Let's take a look at your question.

We have to check the inequalities that hold if 3.24 < x < 5.36
The open interval given includes all the values between 3.24 and 5.36 exclusive.

We will check all the given inequalities for at least two random values of the given interval let's say for x = 3.25 and 5.35
Let's start from option A.
$$\left|x+4.3\right|<1.06$$
$$For\ x=3.25,\ x\ =\ 5.35$$
$$\left|3.25+4.3\right|<1.06,\ \left|5.35+4.3\right|<1.06$$
$$\left|7.55\right|<1.06,\ \left|9.65\right|<1.06$$
$$7.55<1.06,\ 9.65<1.06$$

Option A is incorrect for both values of x.

Let's check option B.
$$\left|x-4.3\right|<1.06$$
$$For\ x=3.25,\ x\ =\ 5.35$$
$$\left|3.25-4.3\right|<1.06,\ \left|5.35-4.3\right|<1.06$$
$$\left|-1.05\right|<1.06,\ \left|1.05\right|<1.06$$
$$1.05<1.06,\ 1.05<1.06$$
Option B is correct for both the values of x.

Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

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### GMAT/MBA Expert

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The inequality |x-a| Note that a is the average of a - b and a + b and b is half of the difference between a - b and a + b, that is, b = {( a + b ) - ( a - b )} / 2.

Thus, the inequality 3.24 < x < 5.36 is equivalent to the inequality | x - 4.3 | < 1.06 since a = ( 3.24 + 5.36 ) / 2 = 8.6 / 2 = 4.3 and b = ( 5.36 - 3.24 ) / 2 = 2.12 / 2 = 1.06.

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