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

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by pzazz12 » Mon Oct 25, 2010 4:05 am
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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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by fskilnik@GMATH » 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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Jeff@TargetTestPrep » 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

Answer: A

Jeffrey Miller
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by [email protected] » Fri Mar 16, 2018 11:09 am
Hi All,

We're told [X] is the GREATEST integer that is LESS than OR EQUAL to X. We're asked for the value of [-1.6] + [3.4] + [2.7]. This is an example of a 'symbolism' question - a symbol is 'made up', we're told what it means and then we're asked to perform a calculation using that symbol. To answer this question, we just have to follow the 'instructions' given by the prompt.

We need the GREATEST integer that is less than or equal to each of the following:
-1.6
3.4
2.7

With -1.6, the greatest integer that is less than or equal to -1.6 would be -2
With 3.4, the greatest integer that is less than or equal to 3.4 would be 3
With 2.7, the greatest integer that is less than or equal to 2.7 would be 2

Thus, the answer is (-2) + 3 + 2 = +3

Final Answer: A

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