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# The difference between the greatest and least possible value

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The difference between the greatest and least possible value [#permalink]  21 Jun 2017, 12:45
Expert's post
00:00

Question Stats:

33% (01:21) correct 66% (00:57) wrong based on 125 sessions

n is an integer, and $$|2n + 7| <= 10$$.

 Quantity A Quantity B The difference between the greatest andleast possible values of n 10

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Last edited by Carcass on 07 Dec 2017, 02:58, edited 3 times in total.
Updated the question
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Re: The difference between the greatest and least possible value [#permalink]  26 Jun 2017, 05:48
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The question is not complete!
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Re: The difference between the greatest and least possible value [#permalink]  27 Jun 2017, 02:03
Expert's post
nainy05 wrote:
The question is not complete!

Thanks to pointed out. Many thanks.
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Re: The difference between the greatest and least possible value [#permalink]  27 Jun 2017, 10:35
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Expert's post
Carcass wrote:

n is an integer, and |2n + 7| ≤ 10.

 Quantity A Quantity B The difference between the greatest andleast possible values of n 10

When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

Given: |2n + 7| ≤ 10
In this case, we'll apply rule #1 to get: -10 ≤ 2n + 7 ≤ 10
Subtract 7 from all three parts: -17 ≤ 2n ≤ 3
Divide all three parts by 2 to get: -8.5 ≤ n ≤ 1.5
Since n is an INTEGER, the possible values of n are: -8, -7, -6, -5,....0, 1

The question:
Quantity A: The difference between the greatest and least possible values of n
Quantity B: 10

We get:
Quantity A: 1 - (-8)
Quantity B: 10

Evaluate:
Quantity A: 9
Quantity B: 10

[Reveal] Spoiler:
B

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Re: The difference between the greatest and least possible value [#permalink]  28 Oct 2017, 00:32
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Little plot twist: if the inequality were $$|2n-7|\geq 10$$, the solution would have been $$n \geq \frac{3}{2}$$ and $$n \leq -\frac{17}{2}$$.
In this case the difference between the highest and smallest values of n would have been 2 - (-9) = 11 so that A would have been greater!
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Re: The difference between the greatest and least possible value [#permalink]  13 Oct 2018, 07:45
Why quantity A is 1-(-8).. plz explain me this step.
thanks
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Re: The difference between the greatest and least possible value [#permalink]  13 Oct 2018, 11:42
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Expert's post
Reetika1990 wrote:
Why quantity A is 1-(-8).. plz explain me this step.
thanks

The smallest integer value that is possible is $$-8$$ and the largest integer value is 1.

So Largest -smallest=$$1- (-8)=9$$
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Re: The difference between the greatest and least possible value   [#permalink] 13 Oct 2018, 11:42
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