GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The mean of 3 numbers 2x, 3x, x^2 is 12, where x<0.
[#permalink]
02 Feb 2022, 22:02
02 Feb 2022, 22:02
1
1
Bookmarks
00:00
Question Stats:
99% (01:19) correct
0% (00:00) wrong based on 7 sessions
Hide Show timer Statistics
The mean of three numbers \(2x\), \(3x\), \(x^2\) is \(12\), where \(x<0\). What is the range of the three numbers?
A. 108
B. 144
C. 176
D. 228
E. 256
Posted from my mobile device
A. 108
B. 144
C. 176
D. 228
E. 256
Posted from my mobile device
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: The mean of 3 numbers 2x, 3x, x^2 is 12, where x<0.
[#permalink]
03 Feb 2022, 07:21
03 Feb 2022, 07:21
2
1
Bookmarks
Sumukh19 wrote:
The mean of three numbers \(2x\), \(3x\), \(x^2\) is \(12\), where \(x<0\). What is the range of the three numbers?
A. 108
B. 144
C. 176
D. 228
E. 256
Posted from my mobile device
A. 108
B. 144
C. 176
D. 228
E. 256
Posted from my mobile device
Given: The mean of three numbers \(2x\), \(3x\), \(x^2\) is \(12\)
So we can write: \(\frac{2x + 3x + x^2}{3} = 12\)
Simplify the numerator: \(\frac{x^2 + 5x}{3} = 12\)
Multiply both sides of the equation by \(3\) to get: \(x^2 + 5x = 36\)
Subtract \(36\) from both sides: \(x^2 + 5x - 36 = 0\)
Factor: \((x + 9)(x - 4) = 0\)
So, either \(x = -9\) or \(x = 4\)
Since we are told \(x<0\), we can be certain that \(x = -9\)
If \(x = -9\), then the values of the three numbers are as follows:
\(2x = 2(-9) = -18\)
\(3x = 3(-9) = -27\)
\(x^2 = (-9)^2 = 81\)
Range = (largest number) - (smallest number)
\(= 81 - (-27)\)
\(= 108\)
Answer: A
gmatclubot
Re: The mean of 3 numbers 2x, 3x, x^2 is 12, where x<0. [#permalink]
03 Feb 2022, 07:21
Moderators:
