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Which of the following inequalities

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by BTGmoderatorDC » Tue Feb 13, 2018 10:19 pm
Which of the following inequalities is equivalent to -2 < x < 4 ?

(A) | x - 2 | < 4
(B) | x - 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above

I'm confused how to set up the formulas here. Can any experts help?

OA B
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by GMATGuruNY » Wed Feb 14, 2018 3:32 am
lheiannie07 wrote:Which of the following inequalities is equivalent to -2 < x < 4 ?

(A) | x - 2 | < 4
(B) | x - 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above
|x-y| = the DISTANCE between x and y

The midpoint between -2 and 4 = the average of -2 and 4 = (-2+4)/2 = 1.
-2 < x < 4 implies that x can be any value between -2 (3 places to the LEFT of 1) and 4 (3 places to the RIGHT of 1).
In other words: the distance between x and 1 must be less than 3.
In math terms:
|x-1| < 3.

The correct answer is B.

Similar problems:
https://www.beatthegmat.com/inequalities-t299234.html
https://www.beatthegmat.com/absolute-val ... 74256.html
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by Brent@GMATPrepNow » Wed Feb 14, 2018 7:36 am
lheiannie07 wrote:Which of the following inequalities is equivalent to -2 < x < 4 ?

(A) | x - 2 | < 4
(B) | x - 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above
We know that, if |something| < b (when b is positive), then -b < something < b
For example, if |2x+1| < 5 , then -b < 2x+1 < 5

We're going to apply the above rule IN REVERSE

Given: -2 < x < 4
Subtract 1 from all parts: -3 < x-1 < 3
So: |x-1| < 3

Answer: B

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Brent
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by [email protected] » Wed Feb 14, 2018 2:58 pm
Hi lheiannie07,

We're asked which of the following inequalities is equivalent to -2 < X < 4. This question can be solved with a bit of 'brute force' and TESTing VALUES.

To start, let's see what happens to each answer when X approaches its MAXIMUM value (re: X gets really close to 4).

Answer A): |X - 2| < 4
Here, as X gets close to 4, |X - 2| gets really close to 2.... but that's not 'close' to the '4' in this inequality. Eliminate Answer A.

Answer B: |X - 1| < 3
Here, as X gets close to 4, |X - 1| gets really close to 3.... which is a match for this inequality. Keep Answer B for now.

Answer C: |X + 1| < 3
Here, as X gets close to 4, |X + 1| gets really close to 5.... but that's greater than the '4' in this inequality. Eliminate Answer C.

Answer D: |X + 2| < 4
Here, as X gets close to 4, |X + 2| gets really close to 6.... but that's greater than the '4' in this inequality. Eliminate Answer D.

At this point, the Answer is either B or E. Let's check see what happens to Answer B as X approaches its MINIMUM value (re: X gets really close to -2).

Answer B: |X - 1| < 3
Here, as X gets close to -2, |X - 1| gets really close to 3.... which is a match for this inequality. Answer B matches the range given by the initial inequality, so it MUST be the answer.

Final Answer: B

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by Scott@TargetTestPrep » Thu Feb 15, 2018 10:35 am
lheiannie07 wrote:Which of the following inequalities is equivalent to -2 < x < 4 ?

(A) | x - 2 | < 4
(B) | x - 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above
We need to go through the inequalities in the answer choices by solving them without the absolute value sign. However, at first glance, we can eliminate choices A and D since there is no way we can still have the 4 on the right hand side of the final answer when we solve the inequality without the absolute value sign (for example, x - 2 < 4 will become x < 6). So let's look at choice B first:

|x - 1| < 3 means x - 1 < 3 or -(x - 1) < 3.

If x - 1 < 3, then x < 4.

If -(x - 1) < 3, then x - 1 > -3 or x > -2.

Therefore, we have -2 < x < 4.

Answer: B

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