Question: v-w

Comment on v-w

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 ?
gmat-admin's picture

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

Answer: C

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

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?
gmat-admin's picture

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,

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.
gmat-admin's picture

Your solution is perfect! Nice work.

Cheers,
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.
gmat-admin's picture

Question link: https://www.beatthegmat.com/is-b-0-t298460.html

That's a great idea. However, you made one small error.
It's true to write: b³ - b² < 0
But, when you factored it, you got: b²(b-1) > 0 (notice that you accidentally reversed the direction of the inequality symbol)

ASIDE: If we had been able to conclude that b>1, then that would be SUFFICIENT to answer the target question (i.e., if b>1, then b is definitely not less than 0)

Cheers,
Brent

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