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If x is a number between -5 and 15

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If x is a number between -5 and 15  [#permalink]

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New post 19 Sep 2017, 08:26
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Question Stats:

79% (01:12) correct 21% (01:19) wrong based on 306 sessions

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If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0
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If x is a number between -5 and 15  [#permalink]

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New post 19 Sep 2017, 10:25
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petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0

We know: -5 < x < 15

To find the range expressed in an absolute value inequality (or equation) you can use a fairly easy method. If needed, sketch a number line.

1) Find the midpoint,* which is 5, exactly halfway between -5 and 15.

2) Think about "distance from" to set up the expression, LHS

|x| = the distance of x from 0 on the number line

Similarly, |x - 5| is the distance of x from 5, the midpoint. (The point from which distance is measured has "moved" from 0 to 5, the midpoint of THIS range.)

That's the LHS

3) RHS?

Now use 5, midpoint, and 10, distance, as the "distance from": -5 is a distance of 10 from 5, and 15 is a distance of 10 from 5

The x here is not inclusive.

The distance of x from 5 cannot be 10 (which would be |x - 5| = 10), but it can be anything up to 10, namely

|x - 5| < 10

ANSWER C

You can check. (In fact, because these numbers are very manageable, if you got really stuck, you could work from the answer choices.)

|x - 5| < 10, remove absolute value bars, check the two cases

Case 1:
x - 5 < 10
x < 15

Case 2:
x - 5 > -10
x > -5

Together: -5 < x < 15 - Correct

ANSWER C

*Midpoint
\(\frac{(-5 + 15)}{2}\) = 5
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If x is a number between -5 and 15  [#permalink]

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New post 19 Sep 2017, 08:37
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petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0


Given, \(-5<x<15\). Add -5 to both sides of the inequality

\(-5-5<x-5<15-5\) or \(-10<x-5<10\)

This can be written as \(|x-5|<10\)

Option C
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Re: If x is a number between -5 and 15  [#permalink]

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New post 21 Sep 2017, 17:25
petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0



It is important to note that, unless mentioned in the prompt, one needs to assume that the endpoints (-5 and 15) are not inclusive. As in, -5<x<15 and NOT \(-5\leq{x}\leq{15}\)
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Re: If x is a number between -5 and 15  [#permalink]

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New post 30 Dec 2018, 09:17
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-5<X<15

Steps to solve

1. Find midpoint of above range. Mid point =\(\frac{(-5+15)}{2}\) =5

2. Find distance from midpoint for any extreme end. Let's take right most point which is \(15\). Distance from mid point is \(15-5= 10\)

Put above values in equation.

\(|x-(mid point)|<distance\) = \(|x-5| < 10\)

Thanks to gmatbusters for providing above method. Similar question to practice: https://gmatclub.com/forum/which-of-the ... 77345.html
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Re: If x is a number between -5 and 15  [#permalink]

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New post 30 Dec 2018, 09:38
I am glad you liked my approach to these type of questions...

ammuseeru wrote:
-5<X<15

Steps to solve

1. Find midpoint of above range. Mid point =\(\frac{(-5+15)}{2}\) =5

2. Find distance from midpoint for any extreme end. Let's take right most point which is \(15\). Distance from mid point is \(15-5= 10\)

Put above values in equation.

\(|x-(mid point)|<distance\) = \(|x-5| < 10\)

Thanks to gmatbusters for providing above method. Similar question to practice: https://gmatclub.com/forum/which-of-the ... 77345.html

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Re: If x is a number between -5 and 15   [#permalink] 30 Dec 2018, 09:38
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