If [x] is the greatest integer less than or equal to x, what is the va

Question

If   is the greatest integer less than or equal to x, what is the value of   +   +  ?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Bunuel · Accepted Answer

Some function rounds DOWN a number to the nearest integer. For example = 1, = 2, = -2, ... Thus, + + = -2 + 3 + 2 = 3. Answer: A. Similar questions to practice: https://gmatclub.com/forum/if-denotes-t ... 32223.html https://gmatclub.com/forum/if-denotes-t ... 94687.html https://gmatclub.com/forum/for-all-numb ... 05416.html https://gmatclub.com/forum/is-x-an-odd- ... 99856.html https://gmatclub.com/forum/for-all-z-de ... 10561.html https://gmatclub.com/forum/denotes-to-b ... 30841.html https://gmatclub.com/forum/for-all-numb ... 05416.html Hope it helps.

JeffTargetTestPrep · Answer

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 the integer 2, because the integer 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 the integer -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  ,  ,and  . Since the notation   means the greatest integer less than or equal to x, we will round down each value in the brackets. Therefore,

= -2

= 3

= 2

We sum these three integers:

-2 + 3 + 2 = 3

Answer is A.

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=EmIQ3QTmVJ8

karanamin · Answer

You are asked what the closest lesser integer value to   is.

= -2.0
  = 3.0
  = 2.0

Therefore , answer is: -2.0 + 3.0 + 2.0 = 3.0

Option A.

infinitemac · Answer

Question - I first approached this question by straight away adding -1.6 + 3.4 + 2.7 but how come we have to find out what each individual value is worth before combining them? Thanks!

Bunuel · Answer

Let me ask you - what is the question:

What is the value of   +   +   = ?

OR

What is the value of   = ?

hopefulmba2021 · Answer

If   is the greatest integer less than or equal to x, shouldn't x be a higher value than  ?
So, IMO
  = -1

= 4

= 3

I am getting confused by the wording in this problem.

Bunuel · Answer

If   is the greatest integer LESS than or equal to x. So,   rounds DOWN a number to the nearest integer:

= -2, because -2 is the greatest integer LESS than or equal to -1.6.

= 3, because 3 is the greatest integer LESS than or equal to 3.4.

= 2, because 2 is the greatest integer LESS than or equal to 2.7.

If it were,   denotes the least integer GREATER than or equal to x, then we should rounds UP a number to the nearest integer. For example  =2 (because 2 is the least integer GREATER than or equal to 1.5),  =2,  =-1, ...

Check similar questions to practice here:  Rounding Functions .

Hope it helps.

Hovkial · Answer

OFFICIAL GMAT EXPLANATION

The greatest integer that is less than or equal to –1.6 is –2. It cannot be –1 because –1 is greater than –1.6. The greatest integer that is less than or equal to 3.4 is 3. It cannot be 4 because 4 is greater than 3.4. The greatest integer that is less than or equal to 2.7 is 2. It cannot be 3 because 3 is greater than 2.7. Therefore,  + + = -2+3+2 = 3

The correct answer is A.

sahuanamika · Answer

It is asked to get the closest lesser integer value of   :

= -2.0 as -2 is less than -1.6
  = 3.0 
  = 2.0

Therefore , answer is: -2.0 + 3.0 + 2.0 = 3.0

Option A.

woohoo921 · Answer

Bunuel 
To confirm, for -1.6, you round down because .6 is greater than .5? If it was -1.4, you would round to -1, correct? Happy Holidays!

egmat · Answer

Hey  woohoo921

You are confusing what Bunuel said with the concepts of rounding up/rounding down as we use in estimation. In estimation, rounding off really does depend on which integer your decimal number is closer to. In that sense, yes, -1.6 would round off to -2, while -1.4 would round off to -1.

But this question is completely different. Here, you have a definition of   and that is all you need to use. Let’s try to understand this in more detail:

For every x, function   in this question is defined as a round down function only. 
  Here, “rounding down x” means going to the nearest integer that is smaller than or equal to x. Irrespective of the value of a number, we will round it to the greatest integer less than or equal to the number.

Let’s see two examples now – both your considerations, -1.4 and -1.6.

x = -1.4: Realize that we want the greatest integer which is less than -1.4. 
  So, out of all the integers less than -1.4, we just need the greatest.  
 This list of integers is {-2, -3, -4, -5, …} and the greatest integer in the list is -2.  
 Hence,   = -2.  
 x = -1.6: Again, we want the greatest integer which is less than -1.6.  
 So, out of all the integers less than -1.6, we need the greatest.  
 The list is the same even now, {-2, -3, -4, -5, …}, and the greatest integer in it is -2.  
 Hence,   = -2 also!

Hope this helps!

Best Regards, 
Ashish 
Quant Expert, e-GMAT

Rahilgaur · Answer

Output of   is
1. an integer
2. less than x.
Hence,   => -2 ,  => 3,  = 2,

Answers ===> -2+3+2= 3

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If [x] is the greatest integer less than or equal to x, what is the va

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If [x] is the greatest integer less than or equal to x, what is the va

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