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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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If x < 20 and x – 8 > x + 4, which of the following expresses th
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25 Nov 2016, 10:44
Question Stats:
74% (01:52) correct 26% (02:03) wrong based on 719 sessions
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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 < 20Absolute 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 InequalitiesMike
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Mike McGarry Magoosh Test Prep
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
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25 Nov 2016, 11:09
B for me.
x < 20 means that 20<x<20.
Now the expression: x – 8 > x + 4 Squaring both sides we get (x8)^2>(x+4)^2 =>x<2 So, combining the 2 ranges, we get –20 < x < 2.




Senior Manager
Joined: 24 Apr 2016
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Re: If x < 20 and x – 8 > x + 4, which of the following expresses th
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06 Feb 2017, 23:20
Given: x < 20 and x – 8 > x + 4, x < 20, so this gives 20 < x < 20 > Ax – 8 > x + 4Here 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 x8 > 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?



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4489

Re: If x < 20 and x – 8 > x + 4, which of the following expresses th
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07 Feb 2017, 10:48
quantumliner wrote: Given: x < 20 and x – 8 > x + 4, x < 20, so this gives 20 < x < 20 > Ax – 8 > x + 4Here 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 x8 > 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 & timeconsuming. It is an extremely reductionist and leftbrain approach, algebraic & formulaic rather than patternbased. See the original post, linked with the problem, for a more patternbased 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 FasterMy friend, you obviously have great algebraic skill. If you can combine these organization & detail management skills with intuition and patternmatching, you will take your math performance to a whole other level. Does all this make sense? Mike
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Mike McGarry Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Senior Manager
Joined: 24 Apr 2016
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Re: If x < 20 and x – 8 > x + 4, which of the following expresses th
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07 Feb 2017, 13:32
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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Joined: 28 Aug 2016
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Re: If x < 20 and x – 8 > x + 4, which of the following expresses th
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10 Nov 2017, 06:07
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 x8>x+4= x8> 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
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22 Jul 2018, 21:08
mikemcgarry wrote: quantumliner wrote: Given: x < 20 and x – 8 > x + 4, x < 20, so this gives 20 < x < 20 > Ax – 8 > x + 4Here 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 x8 > 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 & timeconsuming. It is an extremely reductionist and leftbrain approach, algebraic & formulaic rather than patternbased. See the original post, linked with the problem, for a more patternbased 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 FasterMy friend, you obviously have great algebraic skill. If you can combine these organization & detail management skills with intuition and patternmatching, you will take your math performance to a whole other level. Does all this make sense? Mike Dear mikemcgarry, Could you please show us a shorter/ faster approach please, thanks. I did refer How to do GMAT Math Faster. Cheers.



Intern
Joined: 13 Nov 2018
Posts: 5

Re: If x < 20 and x – 8 > x + 4, which of the following expresses th
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30 Nov 2018, 06:33
Hi mikemcgarry, I'd like to ask you. maybe it is novice question haha. There are only three approaches of +=+, = and =+. Why can't I try to solve for += giving me the range x>2? I'm getting lost here. Could you please explain?




Re: If x < 20 and x – 8 > x + 4, which of the following expresses th &nbs
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30 Nov 2018, 06:33






