docabuzar wrote:

Which of the following represents 1<x<9?

A. |x|<3

B. |x+5|<4

C. |x-1|<9

D. |-5+x|<4

E. |3+x|<5

How to do this quickly? The way I m doing it ( i.e. solving each statement possibilities ) takes 3-4 min.

The below is my approach for any modulus qtn in GMAT. Please read thru the complete explanation to understand the modulus concept.

Remember.

The meaning of |x-y| is "On the number line, the distance between X and +Y"

The meaning of |x+y| is "On the number line, the distance between X and -Y"

The meaning of |x| is "On the number line, the distance between X and 0".

On the # line, Left to 0 are all the -ve #s and right to 0 are all +ve #s

original qtn:

is x between 1 and 9 ==> .....................0..1

....................9..... ==> is X in the highlighted area

A) |x| < 3 ---- wrong

on the number line, the distance of x from 0 is < 3 ==> ......-3

........0........3....

B) |x+5|<4 --- wrong

on the number line, the distance of x from -5 is < 4 ==> ............-9

............-5...........1...0.......3....

C)|x-1|<9 --- wrong

on the number line, the distance of x from 1 is < 9 ==> ..................-8

..............................0....1

.......................9...10....

D) |-5+x|<4

on the number line, the distance of x from +5 is < 4 ==> ............0..1

..............5...............9 ---- This is what is asked in the question, hence, correct answer

E. |3+x|<5