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A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which of

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by BTGmoderatorDC » Wed Jan 11, 2023 1:56 am

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E

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A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set?

(A) 85
(B) 90
(C) 123
(D) 150
(E) 155


OA E

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Re: A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which

by Scott@TargetTestPrep » Wed Jan 11, 2023 9:33 am
BTGmoderatorDC wrote: ↑
Wed Jan 11, 2023 1:56 am
 A set of numbers has an average of 50. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set?

(A) 85
(B) 90
(C) 123
(D) 150
(E) 155


OA E

Source: Veritas Prep
Solution:

We can let the smallest element = n and the largest = 3n + 4. Since the average is 50, then the smallest element, n, must be less than 50. Since n < 50, the largest element, 3n + 4, must be less than 3(50) + 4 = 154. We see that all the numbers in the choices are less than 154 except 155. Thus, 155 can’t be in the set.

Answer: E

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