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If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses th

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If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses th [#permalink]

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If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?

(A) –12 < x < 12

(B) –20 < x < 2

(C) –20 < x < –12 and 12 < x < 20

(D) –20 < x < –8 and 4 < x < 20

(E) –20 < x < –4 and 8 < x < 20


Absolute value inequalities are a rare and tricky category on the GMAT. For a detailed discussion of this topic, as well as the OE for this particular question, see:
Absolute Value Inequalities

Mike :-)
[Reveal] Spoiler: OA

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Mike McGarry
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Re: If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses th [#permalink]

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B for me.

|x| < 20 means that -20<x<20.

Now the expression: |x – 8| > |x + 4|
Squaring both sides we get (x-8)^2>(x+4)^2
=>x<2
So, combining the 2 ranges, we get –20 < x < 2.

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Re: If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses th [#permalink]

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Given: |x| < 20 and |x – 8| > |x + 4|,

|x| < 20, so this gives -20 < x < 20 ------> A

|x – 8| > |x + 4|

Here we have 3 possibilities:

(i) x < -4

-x+8 > - x + 4, as x's cancel out, we don't get a range here.

(ii) -4 < x < 8

-x+8 > x+4
x< 2 -------------> B

(iii) x > 8

x-8 > x+4, , as x's cancel out, we don't get a range here.

Therefore, by combining the ranges A & B, we get -20 < x < 2. Answer: B

mikemcgarry, could you please confirm if the solution is correct?

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Re: If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses th [#permalink]

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quantumliner wrote:
Given: |x| < 20 and |x – 8| > |x + 4|,

|x| < 20, so this gives -20 < x < 20 ------> A

|x – 8| > |x + 4|

Here we have 3 possibilities:

(i) x < -4

-x+8 > - x + 4, as x's cancel out, we don't get a range here.

(ii) -4 < x < 8

-x+8 > x+4
x< 2 -------------> B

(iii) x > 8

x-8 > x+4, , as x's cancel out, we don't get a range here.

Therefore, by combining the ranges A & B, we get -20 < x < 2. Answer: B

mikemcgarry, could you please confirm if the solution is correct?

Dear quantumliner,

I'm happy to respond. :-)

Your approach is 100% correct BUT long & detailed & time-consuming. It is an extremely reductionist and left-brain approach, algebraic & formulaic rather than pattern-based. See the original post, linked with the problem, for a more pattern-based approach to these problems.

It may not have taken very long on this relatively straightforward problem, but having only this approach will create problems for you on some advanced problems. See this post:
How to do GMAT Math Faster
My friend, you obviously have great algebraic skill. If you can combine these organization & detail management skills with intuition and pattern-matching, you will take your math performance to a whole other level.

Does all this make sense?
Mike :-)
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Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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Re: If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses th [#permalink]

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New post 07 Feb 2017, 14:32
Thanks mikemcgarry !! I went through your post and it makes sense. Visual understanding of a problem and to understand what exactlyis happening indeed makes solving the problem faster and easier. I will try to use this method to get a better grip of this technique.

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Re: If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses th [#permalink]

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New post 10 Nov 2017, 07:07
Hello Mr Mike the way approached this problem was;

|x|= 20 is x<20 & x>-20

therefore -20<x<20

now since mode has two solutions |x-8|>x+4= x-8> x+4 would lead to x=0 we'll be only left with

-x+8>x+4 which results in x<2

therefore our answer is -20<x<2 which is B

Is it right??

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Re: If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses th   [#permalink] 10 Nov 2017, 07:07
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