# Question: v-w

## Comment on v-w

### If |x| denotes the least

If |x| denotes the least integer greater than or equal to x,
is |x|=0?
(1) –1 < x < 1
(2) x < 0

hi Brent can u pls explain above problem ? ### Given: [x] denotes the least

Given: [x] denotes the least integer greater than or equal to x.
So, for example, [1.3] = 2, since 2 is the smallest INTEGER that's greater than 1.3
Likewise, [8.8] = 9, since 9 is the smallest INTEGER that's greater than 8.8
[-3.5] = -3, since -3 is the smallest INTEGER that's greater than -3.5
[-0.9] = 0, since 0 is the smallest INTEGER that's greater than -0.9

Target question: Is [x] = 0?
In order for [x] to equal 0, x must be greater than -1 and less than or equal to zero.

So... REPHRASED target question: Is -1 < x ≤ 0?

Statement 1: –1 < x < 1
This is not enough information to answer the REPHRASED target question.
case a: x = -0.5, in which case -1 < x ≤ 0
case b: x = 0.5, in which case 0 < x
Since we cannot answer the REPHRASED target question, statement 1 is NOT SUFFICIENT

Statement 2: x < 0
This is not enough information to answer the REPHRASED target question.
case a: x = -0.5, in which case -1 < x ≤ 0
case b: x = -2, in which case x < -1
Since we cannot answer the REPHRASED target question, statement 2 is NOT SUFFICIENT

Statements 1 and 2 COMBINED
Statement 1 tells us that -1 < x
Statement 2 tells us that x < 0
When we combine these inequalities, we get: -1 < x < 0
PERFECT.
This is EXACTLY what the REPHRASE target question is asking.

Since we can answer the REPHRASED target question, the COMBINED statements are SUFFICIENT

Here's a related question to practice: http://www.beatthegmat.com/number-property-question-t271768.html

### When answering the question I

When answering the question I plugged in numbers in the answer's equations and I had the same answer. Is this is a valid approach? ### Plugging in values yields

Plugging in values yields conclusive results IF doing so yields conflicting answers to the target question, in which case the statement is NOT sufficient.

However, in cases where a statement is sufficient, plugging in values will help us feel more confident about the sufficiency of the statement, but it doesn't yield conclusive results.

More on this here: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

### Hi Brent,

Hi Brent,

Is it possible to do the following:

Leave the question as is and do the following to the statements:

statement 1: v > x and w < y

flip them so that the inequality faces the same way: x < v and w < y
Add them: x + w < v + y
Manipulate them so that it reads: v - w > x - y

Of course the method you have shown is quicker and I'll be using that in the future. I wanted to know if I'm breaking any rules.

Thanks again for your quick responses. Your solution is perfect! Nice work.

Cheers,
Brent

### HI Brent ,

HI Brent ,

for the question @ https://www.beatthegmat.com/is-b-0-t298460.html

i saw your explanation and have one doubt.
While combining the statements the result comes out to be
b³ - b² < 0
on further simplifying
b²(b-1)>0

means b>1 since square of a number can not be negative
so ultimate outcome will be b>1 which is not sufficient to comment that b<0
let me know where i am missing the trick. 