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# If x is a number between -5 and 15

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Intern
Joined: 16 Mar 2017
Posts: 13
If x is a number between -5 and 15  [#permalink]

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19 Sep 2017, 08:26
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Difficulty:

5% (low)

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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Joined: 22 May 2016
Posts: 3565
If x is a number between -5 and 15  [#permalink]

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19 Sep 2017, 10:25
3
2
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

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

*Midpoint
$$\frac{(-5 + 15)}{2}$$ = 5
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##### General Discussion
Retired Moderator
Joined: 25 Feb 2013
Posts: 1178
Location: India
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If x is a number between -5 and 15  [#permalink]

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19 Sep 2017, 08:37
1
2
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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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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Joined: 17 Mar 2014
Posts: 429
Re: If x is a number between -5 and 15  [#permalink]

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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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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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