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If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

Originally posted by avigutman on 04 Oct 2020, 16:15.
Last edited by avigutman on 30 Nov 2020, 14:11, edited 1 time in total.
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Re: If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
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You are asked what the closest lesser integer value to [x] is.

[-1.6] = -2.0
[3.4] = 3.0
[2.7] = 2.0

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

Option A.
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Re: If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
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!
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Re: If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
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infinitemac wrote:
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!


Let me ask you - what is the question:

What is the value of [-1.6] + [3.4] + [2.7] = ?

OR

What is the value of [-1.6 + 3.4 + 2.7] = ?
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Re: If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
If [x] is the greatest integer less than or equal to x, shouldn't x be a higher value than [x]?
So, IMO
[-1.6] = -1

[3.4] = 4

[2.7] = 3

I am getting confused by the wording in this problem.
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Re: If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
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soumyadeeppaul1 wrote:
If [x] is the greatest integer less than or equal to x, shouldn't x be a higher value than [x]?
So, IMO
[-1.6] = -1

[3.4] = 4

[2.7] = 3

I am getting confused by the wording in this problem.


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

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

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

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

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

Check similar questions to practice here: Rounding Functions.

Hope it helps.
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Re: If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
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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, [-1.6]+[3.4]+[2.7]= -2+3+2 = 3

The correct answer is A.
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Re: If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
It is asked to get the closest lesser integer value of [x] :

[-1.6] = -2.0 as -2 is less than -1.6
[3.4] = 3.0
[2.7] = 2.0

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

Option A.
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Re: If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
Bunuel wrote:
soumyadeeppaul1 wrote:
If [x] is the greatest integer less than or equal to x, shouldn't x be a higher value than [x]?
So, IMO
[-1.6] = -1

[3.4] = 4

[2.7] = 3

I am getting confused by the wording in this problem.


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

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

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

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

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

Check similar questions to practice here: Rounding Functions.

Hope it helps.


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!
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If [x] is the greatest integer less than or equal to x, what is the va [#permalink]
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woohoo921 wrote:
Bunuel wrote:
soumyadeeppaul1 wrote:
If [x] is the greatest integer less than or equal to x, shouldn't x be a higher value than [x]?
So, IMO
[-1.6] = -1

[3.4] = 4

[2.7] = 3

I am getting confused by the wording in this problem.


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

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

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

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

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

Check similar questions to practice here: Rounding Functions.

Hope it helps.


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!


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 [x] and that is all you need to use. Let’s try to understand this in more detail:

  • For every x, function [x] 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, [-1.4] = -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, [-1.6] = -2 also!


Hope this helps!


Best Regards,
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