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# X is the set of all integers n that satisfy

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X is the set of all integers n that satisfy [#permalink]  12 Jan 2016, 23:29
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Question Stats:

49% (00:38) correct 50% (00:46) wrong based on 75 sessions
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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Joined: 07 Jun 2014
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Kudos [?]: 1865 [0], given: 397

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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Re: X is the set of all integers n that satisfy [#permalink]  11 Oct 2017, 12:56
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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]  28 Feb 2018, 14:21
It do not require any sort of calculations. Just mental work

Set x = {-5, -4, -3, -2, 2, 3, 4, 5}
Now, absolute value of greatest and least is same i.e 5.

Thus, choice C correct.
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Re: X is the set of all integers n that satisfy [#permalink]  29 Nov 2018, 07:40
@sandy

I need a little understanding. If we take the values seperately e.g the equation can also be translated to
|n|≤5 & 2≤|n|
then
n≤5 or -5≤n & n≤-2 or 2≤n
If we look at the underline set of values, it shows thaat n can be anything greater then/equal to 5 and lesser than/equal to -2. I got answer d. Can you please tell me what i am doing wrong? Thanks!!
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Re: X is the set of all integers n that satisfy [#permalink]  29 Nov 2018, 08:45
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

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

$$2 \leq |n| \leq 5.$$...
so |n| can be 2, 3, 4, 5..
so n = -5, -4, -3, -2, 2, 3, 4, 5
thus the greatest integer will be 5 and |5| = 5
and the smallest integer will be -5 and |-5|=5
thus both are equal

C
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: X is the set of all integers n that satisfy [#permalink]  01 Dec 2018, 06:35
Can i get a link where i can practice similar questions like this?
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Re: X is the set of all integers n that satisfy [#permalink]  01 Dec 2018, 07:26
Expert's post
Click on the tags upon every question

Attachment:

shot26.jpg [ 42.92 KiB | Viewed 1275 times ]

You will have similar questions.

Like this, similar question with the tag absolute value/module

https://greprepclub.com/forum/search.ph ... tag_id=234

Hope this helps.

Regards
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Re: X is the set of all integers n that satisfy [#permalink]  01 Dec 2018, 14:26
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asfandiar wrote:
Can i get a link where i can practice similar questions like this?

See the Tags right above the author there you can click on the tags to get to that collection of questions

For example the Tag inequality is the following link:

https://greprepclub.com/forum/search.php?search_id=tag&tag_id=18&sid=2cc57b3cc9a16dd7273145e1c4f4db2d
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Re: X is the set of all integers n that satisfy   [#permalink] 01 Dec 2018, 14:26
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