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

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

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

Which of the following inequalities holds if \(3.24<x<5.36\)?

\(A. |x+4.3|<1.06\)
\(B. |x-4.3|<1.06\)
\(C. |x-2.1|<0.53\)
\(D. |x+2.1|<0.53\)
\(E. |x-2.1|<1.06\)

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

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New post 08 Feb 2018, 03:22
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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
We have our answer!

(B) is our answer.
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Re: Which of the following inequalities holds if 3.24<x<5.36?  [#permalink]

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New post 08 Feb 2018, 08:36
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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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Re: Which of the following inequalities holds if 3.24<x<5.36?  [#permalink]

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

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New post 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 \(b = \frac{( 5.36 – 3.24 )}{2} =\frac{2.12}{2} = 1.06.\)

Therefore, B is the answer.
Answer: B
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Re: Which of the following inequalities holds if 3.24<x<5.36?  [#permalink]

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Re: Which of the following inequalities holds if 3.24<x<5.36?   [#permalink] 08 Jun 2019, 21:44
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