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## If [x] is the greatest integer..........

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pzazz12 Master | Next Rank: 500 Posts
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#### If [x] is the greatest integer..........

Mon Oct 25, 2010 4:05 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
If [x] is the greatest integer less than or equal to x, what is the value of [-1.6]+[3.4]+[2.7]?

A. 3
B. 4
C. 5
D. 6
E. 7

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### GMAT/MBA Expert

fskilnik GMAT Instructor
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Mon Oct 25, 2010 4:56 am
pzazz12 wrote:
If [x] is the greatest integer less than or equal to x, what is the value of [-1.6]+[3.4]+[2.7]?

A. 3
B. 4
C. 5
D. 6
E. 7
Hi, pzazz12.

Accept my advice: the BEST way to deal safely with this sort of problem is drawing the real number line... doing that, please note that [x] means the value of x itself if x is an integer and the value of the greater integer BELOW x if x is not an integer. That put:

[-1.6] = -2
[3.4] = 3
[2.7] = 2

And you finish it!

Regards,
Fabio.

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### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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Tue Jul 07, 2015 3:36 am
pzazz12 wrote:
If [x] is the greatest integer less than or equal to x, what is the value of [-1.6]+[3.4]+[2.7]?

A. 3
B. 4
C. 5
D. 6
E. 7
Solution:

Remember that an integer is a "whole number" (either positive or negative), or 0. Thus, if we want to know the greatest integer less than or equal to, for example, 2.1, the answer would be 2, because 2, in this case, is the largest integer that is less than 2.1. Similarly, the greatest integer less than -2.4 would be -3, because -3 is the largest integer that is less than -2.4. Note that in each case, we have rounded down, because of the "less than" requirement stated in the question stem.

We first need to determine the values for [-1.6], [3.4], and [2.7]. Since the notation [x] means the greatest integer less than or equal to x, we will round down each value in the brackets. Therefore,

[-1.6] = -2

[3.4] = 3

[2.7] = 2

We sum these three integers:

-2 + 3 + 2 = 3

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