klueless7825 wrote:

For all z,|z| denotes the least integer greater than or equal to z.Is |x| = 0?

(Source:Q 96 - GMAT Quantitative Review 2nd Edition.)

1) -1 < X <-0.1

2) |x+0.5| = 1

How to determine the range for |x+0.5| = 1 ?

I considered two ranges X<0 and X>0.

X>0:

x+0.5 =1

x=0.5

X<0:

-(x+0.5) = 1

x=-1.5

But it looks like I'm missing something.In

OG they have given the range as -0.5<x<=0.5

This is

not a 'modulus' question at all, which is surely the source of your confusion. The question defines a completely different function, one you may never have seen before (sometimes called the 'ceiling function'), and probably won't ever see again (so this question is not likely to be that useful to study). In any case, the question tells us that [x] is equal to the smallest integer which is greater than or equal to x. From that definition, [3.6] would be equal to 4, for example, and [-0.7] would be equal to 0. We just round up the value inside the square brackets to the nearest integer.

So if -1 < x < -0.1, then to find [x], we'd round up to the nearest integer, so we'd round up to 0, and Statement 1 is sufficient. If [x+0.5] = 1, however, we cannot be sure of the value of [x]. It might be that x = 0.2, for example, so [x] is also equal to 1. Or it might be that x = -0.2, in which case [x] = 0. So Statement 2 is not sufficient, and the answer is A.

_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com