Official Solution:

If \(x\) is a negative integer and \(3 \lt x^2 \lt 36\), then what is the value of twice the maximum possible value of \(x\) minus the minimum possible value of \(x\)?

A. \(-12\)
B. \(-9\)
C. \(-3\)
D. \(1\)
E. \(6\)


Since given that \(x\) is a negative integer, then \(x\) can be -2, -3, -4, or -5.

Twice the maximum possible value of \(x\) is \(2*(-2)=-4\).

The minimum possible value of \(x\) is \(-5\).

Thus the answer is \(-4-(-5)=1\).


Answer: D
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I got this right but there can be 2 ways to read the questions -
what is the value of twice the maximum possible value of \(x\) minus the minimum possible value of \(x\)?

Does this mean twice*maximum - minimum (which looks to be the intended explanation) OR
twice* (maximum - minimum) . Unfortunately, both of these are in choices - (1 and 6).

I did 2 (max - min). Ended up with 6 as the answer (incorrect answer) :(

pay attention to where the "twice" is.
if twice was before amount of - then 2 (max-min)
but since twice is after the amount, it clearly only refers to the maximum only
SC :D

question is worded very vaguely. please make the question more specific.

Can you please tell me which part is ambiguous? For me the question is clear.
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Dear Bunuel,

I suggest if you can include an answer choice -8. It is a trap as some would solve: -5*2 +2 = -8.

thanks

Dear Experts why -1 was not taken as maximum value .only -2 was considered..kindly explain

Because -1 does not satisfy 3 < x^2 < 36.
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Ambiguous because the phrase suggests that "twice" is an operational adjective describing 1 noun: "the maximum possible value of x minus the minimum possible value of x." In other words, 2(a-b).

Intended meaning can be clarified by rephrasing question as "...what is the difference between twice the maximum possible value of x and the minimum possible value of x" or "...by what amount does the maximum possible value of x exceed the minimum possible value of x" or any other rewording to make it clear that "twice" is an adjective referring solely to the first noun "max{x}".

Brute force with organization will help in this question

\(3 \lt x^2 \lt 36\)
\(3 \lt -2^2 \lt 36\)
\(3 \lt -3^2 \lt 36\)
\(3 \lt -4^2 \lt 36\)
\(3 \lt -5^2 \lt 36\)

\(Max Value = -2\) & \(Min Value = -5\)

\(Twice Max Value - Min Value = 2 (-2) - (-5) = -4 + 5 = 1\)

Answer: D

I think this is a poor-quality question and I don't agree with the explanation.
Question is ambiguous.
twice max-min could be considered as 2(max-min) or 2max -min

Since, x is a negative integer & 3<x<36, It can take the following values, satisfying the mentioned conditions:

-2,-3,-4, and -5.

Now maximum possible value of x = -2 and
Minimum possible value of x = -5.

Now from the question, we have to calculate the following:
2* (Maximum possible Value of x) - (minimum Possible Value of x)
=> 2* (-2) - (-5)
=> -4 + 5
=> 1

Hence D is the answer.

Agreed, I spent about 90 sec fumbling over whether "What is the value of twice the maximum possible value of x minus the minimum possible value of x?" meant:
a) 2*(Max - Min), or
b) 2*Max - Min

I think this is a high-quality question and I agree with explanation.

I think the question stem is not precise enough as one could think "the value of twice the maximum possible value of xx minus the minimum possible value of x" could mean
2(MAX - MIN) and not 2(MAX) - MIN

I agree with some other posts that the question stem was a little bit confusing in terms of where the "twice" needs to be applied.