If x is a negative integer and 2 < x^2 < 36, what is the least possibl : Problem Solving (PS)

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If x is a negative integer and 2 < x^2 < 36, what is the least possibl

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Math Expert

Joined: 02 Sep 2009

Posts: 56277

If x is a negative integer and 2 < x^2 < 36, what is the least possibl [#permalink]

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23 Apr 2018, 23:48

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GMAT CLUB TESTS' FRESH QUESTION:

If x is a negative integer and 2 < x^2 < 36, what is the least possible value of |2x + 11| ?

A. 7
B. 5
C. 3
D. 1
E. 0

Spoiler: OA

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Math Expert

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Re: If x is a negative integer and 2 < x^2 < 36, what is the least possibl [#permalink]

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04 Jul 2019, 06:57

Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

If x is a negative integer and 2 < x^2 < 36, what is the least possible value of |2x + 11| ?

A. 7
B. 5
C. 3
D. 1
E. 0

OFFICIAL EXPLANATION:

If \(x\) is a negative integer and \(2 < x^2 < 36\), what is the least possible value of \(|2x + 11|\)?

A. 7
B. 5
C. 3
D. 1
E. 0

Notice that we are told that \(x\) is a negative integer. Thus \(x\) can be -2, -3, -4, or -5. The least value of \(|2x + 11|\) for those values of \(x\) is 1, when \(x=-5\).

If we were not told that \(x\) is a negative integer, then the least value will obviously be 0, for \(x=-5.5\).

Answer: D
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Joined: 05 Dec 2017

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Re: If x is a negative integer and 2 < x^2 < 36, what is the least possibl [#permalink]

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24 Apr 2018, 02:53

Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

If x is a negative integer and 2 < x^2 < 36, what is the lest possible value of |2x + 11| ?

A. 7
B. 5
C. 3
D. 1
E. 0

Least possible value of a mod function is 0

Here 0 can be attained by 2x+11 = 0 or x = -5.5, now since x^2 <36, x can't be -6

Hence at x = -5; the value of the function is |-10+11| = 1

Hence D

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Re: If x is a negative integer and 2 < x^2 < 36, what is the least possibl [#permalink]

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25 Apr 2018, 14:59

Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

If x is a negative integer and 2 < x^2 < 36, what is the lest possible value of |2x + 11| ?

A. 7
B. 5
C. 3
D. 1
E. 0

\(2 < x^2 < 36\)

X is negative integer, then \(-6 < x <-\) \(\sqrt{2}\).........It is nice to know \(\sqrt{2}=1.4\)

Then \(-6 < x <-1.4\)... x could be -5, -4, -3, -2......To make least, we need to take +11 down.......So least negative number -5

|2x + 11| = |2*-5 + 11| = |-10 + 11| = 1

Answer: D

Bunuel

Do you add any fresh GMAT Club tests question to the bank of the questions itself directly? or just post here in the forum?

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Joined: 01 Apr 2012

Posts: 16

Re: If x is a negative integer and 2 < x^2 < 36, what is the least possibl [#permalink]

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26 Apr 2018, 00:03

Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION:

If x is a negative integer and 2 < x^2 < 36, what is the lest possible value of |2x + 11| ?

A. 7
B. 5
C. 3
D. 1
E. 0

Given that x is a negative integer and and 2<x^2<36
so the values the X can take that satisfy this condition are -2, -3, -4,-5 i.e 2< (-2)^2 < 36 ; similarly for others
Substituting the values of -2, -3, -4 and -5 in |2x+11|
The lowest number would be when |2(-5) + 11| = 1
Hence D

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Re: If x is a negative integer and 2 < x^2 < 36, what is the least possibl [#permalink]

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04 May 2018, 18:27

So, we are given that x is negative, and that square of x is between 2 and 36. That takes us to some possible values of x, such as -2,-3,-4,-5.
In order to minimize the modulus |2x+11| output, we need to maximize the negative value inside the modulus. That said, the biggest value of x inside the modulus would be -5.

In algebra...
x = -5
|2x+11| =?

|2*(-5)+11| = |-10+11| = 1

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Re: If x is a negative integer and 2 < x^2 < 36, what is the least possibl [#permalink]

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10 May 2018, 03:06

2<x^2<36
X can be -2,-3,-4,-5

We need to make |2x+11| as minimum , it's minimum value is zero
For zero x need to be -5.5 which is not possible as his negative integer

Then plugging values of -2,-3,-4,-5

We get minimum value as 1 for x=-5

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