If x is a negative integer and 2

Question

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

Bunuel · Accepted Answer

Official Solution:

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 . This means  x  can be -2, -3, -4, or -5. The least value of  |2x + 11|  for these values of  x  is 1, when  x=-5 .
 
If we were not told that  x  is a negative  integer , the least value would obviously be 0, for  x=-5.5 .

Answer: D

RohitGoyal1123 · Answer

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

Mo2men · Answer

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?

vikramnugge · Answer

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

robertops · Answer

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

push12345 · Answer

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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Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

CEdward · Answer

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

2 < x^2 < 36 means that when -x is squared that you get one of the following:
x^2 = 4, 9, 16, or 25 ---> x = -2,-3,-4,-5

Plug in the mod and we see that -5 yields the smallest value: 
|2(-5) + 11 | = 1

D.

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

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