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Which of the following is true if -3<x<9?

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Which of the following is true if -3<x<9?  [#permalink]

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New post 15 Nov 2017, 01:54
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[GMAT math practice question]

Which of the following is true \(if -3<x<9\)?

A. \(|x-3|<4\)
B. \(|x-3|<5\)
C. \(|x-3|<6\)
D. \(|x-3|>4\)
E. \(|x-3|>5\)

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Which of the following is true if -3<x<9?  [#permalink]

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New post 15 Nov 2017, 01:59
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MathRevolution wrote:
[GMAT math practice question]

Which of the following is true \(if -3<x<9\)?

A. \(|x-3|<4\)
B. \(|x-3|<5\)
C. \(|x-3|<6\)
D. \(|x-3|>4\)
E. \(|x-3|>5\)


\(-3<x<9\), add both sides of the inequality \(-3\)

\(=> -6<x-3<6\)

or \(|x-3|<6\)

Option C
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Which of the following is true if -3<x<9?  [#permalink]

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New post 15 Nov 2017, 10:09
MathRevolution wrote:
[GMAT math practice question]

Which of the following is true \(if -3<x<9\)?

A. \(|x-3|<4\)
B. \(|x-3|<5\)
C. \(|x-3|<6\)
D. \(|x-3|>4\)
E. \(|x-3|>5\)

1) Find the distance between, then the midpoint of, the endpoints:
\(9 -(-3) = 12\)
\(\frac{12}{2}\)= 6 = midpoint

2) Change the inequality so it relates to 6 and -6. Subtract 3 from each side:
(-3 - 3) < x < (9 - 3)
-6 < x < 6

3) The -3 becomes part of the absolute value expression:
-6 < |x - 3| < 6, or
|x - 3| < 6

The last step just takes the two cases created by the absolute value inequality |x - 3| < 6, and combines them.

That is, -6 < |x - 3| < 6 says "the absolute value of something is less than 6 (and absolute value is nonnegative)," so change it to
|x - 3| < 6


To check: The two cases for |x - 3| < 6 are

LHS: x - 3 > - 6
RHS: x - 3 < 6
Combined:
-6 < x - 3 < 6
-3 < x < 9 = original. Correct

Answer C
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Re: Which of the following is true if -3<x<9?  [#permalink]

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New post 17 Nov 2017, 01:22
=>

|x-a|<b
⟺ -b < x – a < b
⟺ a - b < x < a + b
So, a is the midpoint of the end points a – b and a + b, and
b is half the distance between the end points a – b and a + b.

The midpoint of -3 and 9 is \(\frac{[(-3)+9]}{2} = \frac{6}{2} = 3\). So, \(a = 3\).
Since the distance between -3 and 9 is 12, \(b = \frac{12}{2} = 6\).
Thus, |x-3| < 6.

Therefore, the answer is C.

Answer: C
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Which of the following is true if -3<x<9?  [#permalink]

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New post 09 Mar 2018, 05:53
MathRevolution wrote:
[GMAT math practice question]

Which of the following is true \(if -3<x<9\)?

A. \(|x-3|<4\)
B. \(|x-3|<5\)
C. \(|x-3|<6\)
D. \(|x-3|>4\)
E. \(|x-3|>5\)


You can use estimate here:

Add the ranges given and divide by 2 i.e., (9 + 3)/ 2 = 6

Only answer choice which has 6 at RHS is (C).

This method will work if we have all different number at RHS of inequality, but you can certainly narrow down your choices by this method.

Regular method is to Use POE and eliminate every answer choices.
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Which of the following is true if -3<x<9?   [#permalink] 09 Mar 2018, 05:53
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