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Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the

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by BTGmoderatorDC » Mon Feb 08, 2021 4:49 pm

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Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

A. 78
B. 77 1/5
C. 66 1/7
D. 55 1/7
E. 52


OA A

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Re: Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the

by swerve » Tue Feb 09, 2021 3:13 am
BTGmoderatorDC wrote: ↑
Mon Feb 08, 2021 4:49 pm
 Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

A. 78
B. 77 1/5
C. 66 1/7
D. 55 1/7
E. 52


OA A

Source: Manhattan Prep
Let smallest \(\# = x,\) Largest \(= 3x + 20\)

So range \(= 2x + 20\)

\(x, x, 55, 55, 3x+20,\) For Max range lowest should be as low as possible and highest should be as high as possible.

Also, the \(2\)nd value has to be minimized, so it is \(x,\) the fourth value also \(ahs\) to be kept at minimum, so it is \(55\)

\(3x + 20 + 110 + 2x = 275\)

\(\Longrightarrow 5x = 275 - 130 = 145 \Longrightarrow x = 29,\) so range \(= 29*2 + 20 = 78\)
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Re: Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the

by Scott@TargetTestPrep » Thu Feb 18, 2021 10:42 am
BTGmoderatorDC wrote: ↑
Mon Feb 08, 2021 4:49 pm
 Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

A. 78
B. 77 1/5
C. 66 1/7
D. 55 1/7
E. 52


OA A

Solution:

The sum of the five numbers is 55 * 5 = 275. If we let x be the smallest number, then the largest number is 3x + 20. Since we want to find the largest possible range, we also want the second smallest number to be the same as the smallest number and the second largest number the same as the median. Therefore, we can create the equation.

x + x + 55 + 55 + 3x + 20 = 275

5x + 130 = 275

5x = 145

x = 29

Since the largest number is 3(29) + 20 = 107 and the smallest number is 29, the largest possible range is 107 - 29 = 78.

Answer: A


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