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X is the set of all integers n that satisfy

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Joined: 07 Jun 2014
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GRE 1: 323 Q167 V156
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X is the set of all integers n that satisfy [#permalink]  12 Jan 2016, 23:29
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X is the set of all integers n that satisfy the inequality 2 \leq |n| \leq 5.

 Quantity A Quantity B The absolute value of the greatest integer in X The absolute value of the least integer in X

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 7
Page:331
Difficulty: easy
[Reveal] Spoiler: OA

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Sandy
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CEO
Joined: 07 Jun 2014
Posts: 2649
GRE 1: 323 Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 42

Kudos [?]: 742 [0], given: 127

Re: X is the set of all integers n that satisfy [#permalink]  13 Jan 2016, 00:05
Expert's post
Solution

When comparing these quantities, it is important to remember that a nonzero number and its negative have the same absolute value. For example, ⎪−2⎪=⎪2⎪=2.

Keeping this in mind, you can see that the positive integers 2, 3, 4, and 5 and the negative integers −2, −3, −4, and −5 all satisfy the inequalities
2 ≤ ⎪n⎪ ≤ 5, and that these are the only such integers. Thus, the set X consists of the integers −5, −4, −3, −2, 2, 3, 4, and 5. The greatest of these integers is 5, and its absolute value is 5. The least of these integers is −5, and its absolute value is also 5. Therefore, Quantity A is equal to Quantity B. The correct answer is Choice C.
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Sandy
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Re: X is the set of all integers n that satisfy [#permalink]  11 Oct 2017, 12:56
Expert's post
sandy wrote:
X is the set of all integers n that satisfy the inequality 2 \leq |n| \leq 5.

 Quantity A Quantity B The absolute value of the greatest integer in X The absolute value of the least integer in X

We're told that n is an INTEGER

Given: 2 ≤ |n| ≤ 5
First recognize that n = 2, n = 3, n = 4 and n = 5 all satisfy the given inequality.

Next notice that some NEGATIVE values work too.
For example, |-2| = 2, so it's true that 2 ≤ |-2| ≤ 5. So, x = -2 is a possible solution
Likewise, |-3| = 3, so it's true that 2 ≤ |-3| ≤ 5. So, x = -3 is a possible solution
And |-4| = 4, so it's true that 2 ≤ |-4| ≤ 5. So, x = -4 is a possible solution
And |-5| = 5, so it's true that 2 ≤ |-5| ≤ 5. So, x = -5 is a possible solution

Set X = {-5, -4, -3, -2, 2, 3, 4, 5}

Quantity A: The absolute value of the greatest integer in X
Quantity B: The absolute value of the least integer in X

The GREATEST integer = 5
The LEAST integer = -5

So, we get:
Quantity A: |5|
Quantity B: |-5|

Evaluate to get:
Quantity A: 5
Quantity B: 5

[Reveal] Spoiler:
C

Cheers,
Brent
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Re: X is the set of all integers n that satisfy   [#permalink] 11 Oct 2017, 12:56
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