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
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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Solution:BTGmoderatorDC wrote: ↑Wed Jan 11, 2023 1:56 amA 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
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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