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Which of the following inequalities holds if 3.24<x<5.

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Max@Math Revolution Legendary Member
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Which of the following inequalities holds if 3.24<x<5.

Post Thu Feb 08, 2018 12:06 am
[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

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Post Thu Feb 08, 2018 4:34 am
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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Max@Math Revolution Legendary Member
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Post Sun Feb 11, 2018 4:49 pm
=>

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.

Therefore, B is the answer.
Answer: B

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