D01-42

Question

If  x  is an integer and  9 < x^2 < 99 , what is the difference between the maximum and minimum possible values of  x ?

A.  5 
B.  8 
C.  13 
D.  18 
E.  20

Bunuel · Accepted Answer

Official Solution:

If  x  is an integer and  9 < x^2 < 99 , what is the difference between the maximum and minimum possible values of  x ?

A.  5 
B.  8 
C.  13 
D.  18 
E.  20

Notice that  x  can take both positive and negative integer values to satisfy  9 < x^2 < 99 . The possible values of  x  are: -9, -8, -7, -6, -4, 4, 6, 7, 8, and 9. We need to find the difference between the maximum and minimum possible values of  x . Since  x_{max} = 9  and  x_{min} = -9 , the difference is  x_{max} - x_{min} = 9 - (-9) = 18 .

Answer: D

amenon55 · Answer

but the questions is asking about x not x^2 though

chdeepak96 · Answer

9 < x^2 < 99
 
Take the square root of all sides. Now when you take the square root of a number you get a positive and a negative root: √9 = ±3 and √99 ≅ ±9.95. This produces two intervals for x:
 
-9.95 < x < -3 and 3 < x < 9.95
 
Since x is an integer, its maximum value is x = 9 and its minimum value is x = -9
 
(Max Value of x) - (Min Value of x) = 9 - (-9) = 9 + 9 = 18

y4nkee · Answer

Good question.
Need to consider the negative values as well...

taruniiita · Answer

x can take positive, as well as negative values

One should always consider all possible cases in mind.

tae808 · Answer

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

Lostre8 · Answer

This is a high-quality and "tricky" question.

sanjay1810 · Answer

This is a definitely a high quality question and I agree with the explanation.

psaikrishna90 · Answer

Very good, tricky and gmat kind of a question. Sad to see people are judging it as a poor quality question without properly understanding/thinking through the solution

ZoeyBishop · Answer

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

D33T · Answer

Bunuel : Not sure if I'm misunderstanding, but I thought GMAT's mathematical rules require us to disregard negative roots? 
This means that the only acceptable derivation of  9 < x^2 < 99  -->  3 < x < 9.9... 
Which makes the maximum minus minimum = 9 - 3 = 6

Ans: B

Bunuel · Answer

\sqrt{nonnegative \ number}\geq 0  but  x^2 = 9  has TWO solutions, +3 and -3. Because  x^2 = 9  means that  x =-\sqrt{9}=-3  or  x=\sqrt{9}=3 .

Sud2021 · Answer

Hi Bunuel , I am not sure if I am satisfied with the explanations provided (not saying that the explanations provided here are incorrect, I am sure they are correct). I feel I still have some gaps in clarity. I found my reasoning to correct answer as the following and please correct me if I am wrong somewhere. So we arrive at x having the following as the values after taking the square root of all the sides √9 = ±3 and √99 ≅ ±9.95. This produces two ranges for both sides when considering both sides independently. -3 > x > 3 and -9.95 < x < 9.95 When we plot these two ranges on a number line then we get a maximum integer value of x = 9 and a minimum value of x = -9 So since the question asked the difference between Max and Min, hence, (Max Value of x) - (Min Value of x) = 9 - (-9) = 9 + 9 = 18 So I have a couple of questions 1. Is my reasoning and thought process correct? 2. When we are given a question where the variable has a range on both sides like we have in this question, can I consider both sides independently and derive the range and then look at both ranges together on the number line? Thanks, Sud

Bunuel · Answer

√9 = 3 only and √99 = 9.somethin only! The square root sign CANNOT given negative result.

You could take the square root from  9 \lt x^2 \lt 99  and you'd get  9 \lt |x| \lt 9.something , hence  x  can be: -9, -8, -7, -6, -5, -4, 4, 5, 6, 7, 8, or 9.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

achloes · Answer

9 < x^2 < 99 
9 < x^2 ≤ 81 (because x is an integer)

Since x is raised to an even exponent, x can be positive or negative.

Possible pos values of x = 4, 5, 6, 7, 8, 9
Possible neg values of x = -4, -5, -6, -7, -8, -9

Max possible value = 9 
Min possible value = -9 
Difference: 9-(-9) = 18

BottomJee · Answer

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

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

D01-42

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards