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# Which of the following inequalities holds if 3.24<x<5.36?

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Math Revolution GMAT Instructor
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Which of the following inequalities holds if 3.24<x<5.36? [#permalink]

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08 Feb 2018, 00:13
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[GMAT math practice question]

Which of the following inequalities holds if $$3.24<x<5.36$$?

$$A. |x+4.3|<1.06$$
$$B. |x-4.3|<1.06$$
$$C. |x-2.1|<0.53$$
$$D. |x+2.1|<0.53$$
$$E. |x-2.1|<1.06$$
[Reveal] Spoiler: OA

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Re: Which of the following inequalities holds if 3.24<x<5.36? [#permalink]

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08 Feb 2018, 03:22
MathRevolution wrote:
[GMAT math practice question]

Which of the following inequalities holds if $$3.24<x<5.36$$?

$$A. |x+4.3|<1.06$$
$$B. |x-4.3|<1.06$$
$$C. |x-2.1|<0.53$$
$$D. |x+2.1|<0.53$$
$$E. |x-2.1|<1.06$$

As the question ask about the range for which an inequality is true, we'll test the extreme values.
This is a Logical approach.

(A) If x = 3.24 then |x + 4.3| is larger than 7, so it is definitely larger than 1.06.
Eliminated.
(B) If x = 3.24 then |x - 4.3| is exactly 1.06 so x > 3.24, means |x - 4.3| < 1.06
Let's try the other extreme: If x = 5.36 then |x - 4.3| is exactly 1.06 so x < 5.36, means |x - 4.3| < 1.06

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Re: Which of the following inequalities holds if 3.24<x<5.36? [#permalink]

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08 Feb 2018, 08:36
MathRevolution wrote:
[GMAT math practice question]

Which of the following inequalities holds if $$3.24<x<5.36$$?

$$A. |x+4.3|<1.06$$
$$B. |x-4.3|<1.06$$
$$C. |x-2.1|<0.53$$
$$D. |x+2.1|<0.53$$
$$E. |x-2.1|<1.06$$

as $$x$$ is a positive number greater than $$3.24$$, so adding any positive number will further increase the value. Hence options A & D can be eliminated because adding positive number to $$x$$ will not yield a positive number lower than $$3.24$$

Option C & E have same LHS

we have $$x>3.24$$ subtract $$2.1$$ from both sides to get

$$x-2.1>3.24-2.1 => x-2.1>1.14$$

so $$|x-2.1|$$ can never be less than $$0.53$$ or $$1.06$$, hence eliminate option C & E

Option B
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Posts: 5649
Re: Which of the following inequalities holds if 3.24<x<5.36? [#permalink]

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08 Feb 2018, 09:01
MathRevolution wrote:
[GMAT math practice question]

Which of the following inequalities holds if $$3.24<x<5.36$$?

$$A. |x+4.3|<1.06$$
$$B. |x-4.3|<1.06$$
$$C. |x-2.1|<0.53$$
$$D. |x+2.1|<0.53$$
$$E. |x-2.1|<1.06$$

Hi...
Modulus does not mean anything except at B..
Others can be taken as normal equation..

One way will be to take 4 or 5 as the value..
Only B.. x-4.3 that is 5-4.3=0.7<1.6 stands

The choices itself give you answer..
X is positive, so when you add something POSITIVE to it, the value has >that POSITIVE value..
So x+4.3<1.06 and X+2.1<0.53 can be discarded.
In all choices, x-4.3 is the smallest as we are subtracting max amount of 4.3 from a positive value x..
So if any other choice matches, even x-4.3 will be true..but we can't have two Answers..
So ans x-4.3
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Which of the following inequalities holds if 3.24<x<5.36? [#permalink]

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11 Feb 2018, 16:59
=>

The inequality $$|x-a|<b$$ is equivalent to the inequality $$a - b < x < a + b.$$
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, $$b = \frac{{( a + b ) – ( a – b )}}{2}.$$

Thus, the inequality $$3.24 < x < 5.36$$ is equivalent to the inequality $$| x – 4.3 | < 1.06$$ since $$a = \frac{( 3.24 + 5.36 )}{2} = \frac{8.6}{2} = 4.3$$ and $$b = \frac{( 5.36 – 3.24 )}{2} =\frac{2.12}{2} = 1.06.$$

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Re: Which of the following inequalities holds if 3.24<x<5.36?   [#permalink] 11 Feb 2018, 16:59
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