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Sajjad1994
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For all numbers N, let N ∞ denote the least integer greater than or eq 04 Jul 2019, 01:43
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C
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81% (00:43) correct 19% (00:46) wrong based on 81 sessions

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For all numbers \(N\), let \(N∞\) denote the least integer greater than or equal to \(N\). What is the value of \(−2.1∞\) ?

(A) –4
(B) –3
(C) –2
(D) –1
(E) 0

Source: Nova GMAT
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C
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For all numbers N, let N ∞ denote the least integer greater than or eq 04 Jul 2019, 01:50
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SajjadAhmad
For all numbers \(N\), let \(N∞\) denote the least integer greater than or equal to \(N\). What is the value of \(−2.1∞\) ?

(A) –4
(B) –3
(C) –2
(D) –1
(E) 0

Source: Nova GMAT
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question says ; \(N\), let \(N∞\) denote the least integer greater than or equal to \(N\)
so for \(−2.1∞\)
IMO C; -2
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For all numbers N, let N ∞ denote the least integer greater than or eq 29 Apr 2020, 21:30
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I still don't understand the questions, does anybody have any link where i can learn the theory of these kind of questions.

I would appreciate it.
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For all numbers N, let N ∞ denote the least integer greater than or eq 30 Apr 2020, 00:14
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Hello Alvarito,

Like any other function, the least integer function is also a function which takes an input and provides an output. However, what’s unique about the least integer function is that it always provides an INTEGER as an output, regardless of what kind of value is given as an input.

The least integer function is defined as – the function that gives the least integer greater than or equal to the value of the input. This is the function that has been defined as N∞ in this question.

Let’s take some examples. If N = 2.5, what do you think is the smallest integer greater than 2.5? Clearly, that’s 3. Therefore, 2.5∞ would yield 3 as the output.
If N = -2.5, the smallest integer greater than -2.5 would obviously be -2. Therefore, -2.5∞ would yield -2 as the output.
If N = -1, the smallest integer equal to -1 would be -1 itself. Therefore, -1∞ would yield -1 as the output.

From the examples above, let’s summarize a few things:

    If the input is an integer, the output would be the same integer.
    If the input is a fraction, the output would be the closest integer to the right of the fraction on the number line.

The best way to deal with ‘least integer function’ questions is to:
    Plot the given number on the number line
    If the given number is a fraction/decimal, select your answer as the first integer to the right of the fraction/decimal.
    If the given number is an integer, select your answer as the integer itself.

In this question, -2.1∞ will clearly be -2. The correct answer option is C.
Hope that helps!
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For all numbers N, let N ∞ denote the least integer greater than or eq 30 Apr 2020, 11:17
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ArvindCrackVerbal
Hello Alvarito,

Like any other function, the least integer function is also a function which takes an input and provides an output. However, what’s unique about the least integer function is that it always provides an INTEGER as an output, regardless of what kind of value is given as an input.

The least integer function is defined as – the function that gives the least integer greater than or equal to the value of the input. This is the function that has been defined as N∞ in this question.

Let’s take some examples. If N = 2.5, what do you think is the smallest integer greater than 2.5? Clearly, that’s 3. Therefore, 2.5∞ would yield 3 as the output.
If N = -2.5, the smallest integer greater than -2.5 would obviously be -2. Therefore, -2.5∞ would yield -2 as the output.
If N = -1, the smallest integer equal to -1 would be -1 itself. Therefore, -1∞ would yield -1 as the output.

From the examples above, let’s summarize a few things:

    If the input is an integer, the output would be the same integer.
    If the input is a fraction, the output would be the closest integer to the right of the fraction on the number line.

The best way to deal with ‘least integer function’ questions is to:
    Plot the given number on the number line
    If the given number is a fraction/decimal, select your answer as the first integer to the right of the fraction/decimal.
    If the given number is an integer, select your answer as the integer itself.

In this question, -2.1∞ will clearly be -2. The correct answer option is C.
Hope that helps!
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Thank you so much for the info, I read it all, now I understand "the least integer function".

Thanks for taking the time to respond.
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For all numbers N, let N ∞ denote the least integer greater than or eq 03 May 2020, 05:56
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SajjadAhmad
For all numbers \(N\), let \(N∞\) denote the least integer greater than or equal to \(N\). What is the value of \(−2.1∞\) ?

(A) –4
(B) –3
(C) –2
(D) –1
(E) 0

Source: Nova GMAT
Show more

The least integer greater than or equal to -2.1 is -2.

Answer: C
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