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18 Apr 2019, 02:06
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:48) correct
33%
(03:01)
wrong
based on 229
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Of the 7 positive integers, the average is 68, the median is 84, and the largest number if 14 more than four times of the smallest number. What is the greatest possible value of the largest number?
(A) 96
(B) 120
(C) 134
(D) 148
(E) 162
(A) 96
(B) 120
(C) 134
(D) 148
(E) 162
24 Jan 2021, 06:51
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rohan2345
Of the 7 positive integers, the average is 68, the median is 84, and the largest number if 14 more than four times of the smallest number. What is the greatest possible value of the largest number?
(A) 96
(B) 120
(C) 134
(D) 148
(E) 162
Solution:(A) 96
(B) 120
(C) 134
(D) 148
(E) 162
We can let the smallest number be s. Thus, the largest number is 4s + 14. We know that the sum of the seven numbers is 68 x 7 = 476 and that one of the numbers (the median) is 84. Furthermore, since we want the largest number to be as large as possible, we want the other numbers to be as small as possible. Thus, we let each of the 3 smallest numbers be s (the value of the smallest number) and each of the next three numbers be 84 (the value of the median). Thus, we can create the equation for the sum of the 7 integers:
s + s + s + 84 + 84 + 84 + (4s + 14) = 476
7s + 266 = 476
7s = 210
s = 30
Therefore, the greatest possible value of the largest number is 4s + 14 = 4 x 30 + 14 = 134.
Answer: C
General Discussion
JayGMATFOCUS
25 Dec 2023, 10:31
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Question stem gives us the info that the largest number (say "g") is 14 more than the smallest number (say "a")
That gets us to the eqn g = 14 + 4a
Simply plug in integers for "a" to check which of the five answer choices we could arrive at (for instance if we assume a=20, then we arrive at g=94 and can therefore eliminate option a with confidence)
With this plugging in values method, we see that only option "c" is possible to satisfy the equation by assuming a=30 (g = 14 + 4*30) = 134.
Therefore Option C is correct
That gets us to the eqn g = 14 + 4a
Simply plug in integers for "a" to check which of the five answer choices we could arrive at (for instance if we assume a=20, then we arrive at g=94 and can therefore eliminate option a with confidence)
With this plugging in values method, we see that only option "c" is possible to satisfy the equation by assuming a=30 (g = 14 + 4*30) = 134.
Therefore Option C is correct
