a,b and c are numbers such that a

Question

a,b and c are numbers such that a<|x+b|<c if and only if -2<x<3 or 12<x<17. What is the value of a+2b+c ?

(A) -1 (B) 0 (C) 1 (D) 2 (E) none of the above

Matrix02 · Answer

Hmmm - very tricky. I am tempted by E. 

Kevin - how would you solve this one?

mukeshnathani · Answer

I would also go with E. Assuming a value for x , say x=-1,b=2 so a can be assumed anything less than 1 , I suppose a=0, and c can be assumed anything > 1 , I assume c=3.Hence the condition a<|x+b|<c and 2<x<3 are satisfied. Solving for a+2b+c = 0 + 4 + 3=7. For different assumed values the answer for a+2b+c is different. Hence I go with option E. Please correct me if I'm wrong.

kevincan · Answer

Clue: What does the solution set of 2<|x-4|<5 look like? Plot it on an number line

Matrix02 · Answer

Ok for 2<|x-4|<5 to be true then X can equal 7,8,0 or -1 right?

tennis1ball · Answer

I got A. <img src="{SMILIES_PATH}/icon_confused.gif" alt=":?" title="Confused" />

Matrix02 · Answer

Kevin - can you exlain the answer please. Thanks

tennis1ball · Answer

Let me explain how I got A.

x+b could be negative or positive. (0 is treated as positive.)

so |x+b| should be either x+b, or -x-b.

1) if a < x+b < c, we get a-b <x < c-b.
then treat a-b and c-b as the 4 numbers in the inequalities. but it is not clear to see the value of a+2b+c.


2). if a < -x-b < c, we get -c-b < x < -a-b. then treat -c-b and -a-b as the ends in the inequalities. Here, we can easily get the value of a+2b+c. and there is a match in the answer choices. so I just pick A.
Note: there could be other answers, but I already found A as a possible one, so why would I bother further. A is definitely alright.

keeeeeekse · Answer

Tennis ball,

i understand your reasoning up to if a < -x-b < c, we get -c-b < x < -a-b. then treat -c-b and -a-b as the ends in the inequalities. Here, we can easily get the value of a+2b+c

how did you get to -1 from there? i know a+2b+c=(-1)-c-2b-a, but since there is no value given at all, how did you get to the final answer?

i am puzzled!!!

tennis1ball · Answer

At this step, I just let -c-b = -2, and -a-b = 3. 
then add these two equations, we get -(a+c-2b) = 1. then i got the result of -1.

jeunesis · Answer

-2<x<3 if x = 0, a=-2, b=1, c= 2 a+2b+c =2...

kevincan · Answer

Notice that the two intervals are equal in length- we can imagine them as the set of points that are between k and k+5 units from the centre of the gap between 3 and 12 (i.e. 7.5) 12 is 4.5 units from 7.5 and 17 is 9.5 units from 7.5, so we can write the solution set as

4.5<|x-7.5|<9.5, so a+2b+c= 14-15=-1

tennis1ball · Answer

the key words is "if and only if", which means the expression of x and its solution are IDENTICAL. so I can substitute the a,b,c expressions with the end points.

a,b and c are numbers such that a<|x+b|<c if and only

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards