Three positive integers a, b and c are such that their average is 20 and a < b < c.
If the median is (a + 11), what is the least possible value of c?
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GMAT Club Forum Index Problem Solving (PS)
Three positive integers a, b, and c are such that their average is 20 : Problem Solving (PS)
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Bunuel
EXPERT'S
POST
Jan 30, 2016
00:00ABCDE
DIFFICULTY: 75% (hard) QUESTION STATS: based on 208 sessions
63% (02:42) correct
37% (02:46) wrong
Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
A. 23
B. 21
C. 25
D. 26
E. 24
Spoiler: OA
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Most Helpful Expert Reply
DmitryFarber
EXPERT'S
POST
Jan 30, 2016
We can solve algebraically without testing values:
a+b+c=60
a ≤ b ≤ c
b=a+11
c=60-(2a+11)
b ≤ c
a+11 ≤ 60-(2a+11)
3a ≤ 38
a ≤ 12 (since it must be an integer)
So the maximum values of a & b are 12 and 23, making the minimum value of c 25.