This is a poorly written question and I am pretty certain that it was not written by real GMAT test writers. The question should be phrased as:
Which of the following inequalities is equivalent to -1<x<5?
The way the original question is phrased, it is asking which of the choices must be true if x falls between -1 and 5, and both B and E hold true. The choice B also satisfies numbers that are outside the original inequality, for example x = -4.
Let's look at a real GMAT question that is related, this one is from GMAT Paper Tests.
Which of the following inequalities is equivalent to -2<x<4?
a) |x-2|<4
b) |x-1|<3
c) |x+1|<3
d) |x+2|<4
e) None of the above
Here the correct answer is B, and the trap answer is A. The answer choice A is equivalent to -2<x<6, which includes all the values that are possible in the original inequality -2<x<4, which means it satisfies all the possible values of x. However, |x-2|<4 is not equivalent to -2<x<4.
And finally how do we turn -2<x<4 to |x-2|<4, first find the mid point of -2 and 4, it is 1, which is 3 units from -2 and 4, then x is the set of all points that is 3 or less units from 1. In geometric terms, |x-1| represents the distance between point x and point 1 on the number line, therefore the original inequality is equivalent to |x-1|<3.
In summary, don't waste your time on questions outside of Official GMAT questions, they are often imprecise, poorly written, and outside the scope of the test.
Dabral
Lasve wrote:Which of the following inequalities must be true if the values of X are between -1 and 5?
|3-x| < -3
-1 <|x|<5
|x| -2 > 2
|2+x| >3
|x-2| <3
OA E
But Actually also B seems good to mean, If X is between -1 and 5 so it will be it's abs value!
Is it just the question that is not very well explained??
Thanks
