Data Sufficiency Problem..

Question

Hi There,

I'm new and this is my first post. Im stuck on a question, which looks easy but I am having trouble understanding what its asking. The questions is:

"If [x] denotes the greatest integer less than or equal to x, is [x] = 0?
1) 5x + 1 = 3 + 2x
2) 0 < X < 1

I know in statement 1 x is 2/3 but don't understand the question. The answer is D. Can anyone help?

Thanks!

logitech · Answer

"If [x] denotes the greatest integer less than or equal to x, is [x] = 0?

1) 5x + 1 = 3 + 2x

3x=2 so X is 2/3. 0.6

0 ... 0.6.......1

[x] denotes the greatest integer less than or equal to x

So yes [x] can be 0 SUF

2) 0 < X < 1

Same logic with the first statement

0......x........1

[x] denotes the greatest integer less than or equal to x

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

odod · Answer

If [x] denotes the greatest integer less than or equal to x,

Does [x] mean absolute value?

Im just trying to make sense of the question; im trying to sub [x] with a number

So does [9] denote the greatest integer less than or equal to 9? i dont get it..

I think im overlooking something really simple here; let me know if you see it.

dipla · Answer

Here the question is - "IS [X]=0" ?

You have to answer yes or no.

Firstly you know if x is between -1 and 0 then only [X]=0 or else it will be
[X] not equal to 0.

1) x=0.6 ( Our answer No , it is not 0 )
2) x between 0 and 1 ( Our answer No, it is not 0 )

So in both cases you are able to answer (without doubts) So we can answer the question with any given condition- D

Ian Stewart · Answer

odod wrote:If [x] denotes the greatest integer less than or equal to x,

Does [x] mean absolute value?

Im just trying to make sense of the question; im trying to sub [x] with a number

So does [9] denote the greatest integer less than or equal to 9? i dont get it..

Yes, exactly: [9] is the greatest integer which is less than or equal to 9. What is the largest integer which is less than or equal to 9? It's 9. Essentially the [ ] function just rounds down to the nearest integer: [5.8] = 5, [17.1] = 17, [-0.3] = -1. The [ ] function is not in any way related to absolute value.

Now, in the question, from the first statement you can get a numerical answer for x, so you can certainly answer any question about x (even if you don't understand what the [ ] does precisely, hopefully it's clear that this statement is sufficient). The second statement tells us that 0 < x < 1, and if this is true, no matter what x is, [x] will round down to 0.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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odod · Answer

thanks gentlemen...makes sense now.

r321 · Answer

Ian Stewart wrote:odod wrote:If [x] denotes the greatest integer less than or equal to x, Does [x] mean absolute value? Im just trying to make sense of the question; im trying to sub [x] with a number So does [9] denote the greatest integer less than or equal to 9? i dont get it.. Yes, exactly: [9] is the greatest integer which is less than or equal to 9. What is the largest integer which is less than or equal to 9? It's 9. Essentially the [ ] function just rounds down to the nearest integer: [5.8] = 5, [17.1] = 17, [-0.3] = -1. The [ ] function is not in any way related to absolute value. Now, in the question, from the first statement you can get a numerical answer for x, so you can certainly answer any question about x (even if you don't understand what the [ ] does precisely, hopefully it's clear that this statement is sufficient). The second statement tells us that 0 < x < 1, and if this is true, no matter what x is, [x] will round down to 0. Hi, I came across this question in OG12 as well. While I managed to solve the question correctly, reading the official answer explanation has confused me. It says "It will be useful to observe that the condition [x] = 0 is equivalent to 0 ≤ x < 1." How?? I don't understand! Can someone please help me understand how [x] = 0 is equivalent to 0 ≤ x < 1 .. Thanks!!

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