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Descriptive statistics
Mean and Median
Problem solving
GMAT QUANTITATIVE REASONINGQ-51 Series
Question
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
a, b, and c are integers; a + b + c = 60; a ≤ b ≤ c; median is (a + 11)
What is the least possible value of c?
1. a, b, and c positive integers.
Given Data
2. Average of a, b, and c = 20.
· So, a + b + c
3= 20 or a + b + c = 60.
3. a ≤ b ≤ c
4. Median, b = (a + 11).
What is the least possible value of c?
· a + (a + 11) + (a + 11) = 60 · Or 3a = 38 or a = 12.66 · So, b = c = 12.66 + 11 = 23.66
a, b, and c are integers; a + b + c = 60; a ≤ b ≤ c; median is (a + 11)
Iteration 1: c = b
Note 2b, the median is (a + 11);
b = c. So, c is also (a + 11)
Note 1The lowest value possible for c is
equating it to b because b < c
What is the least possible value of c?
· a + (a + 11) + (a + 11) = 60 · Or 3a = 38 or a = 12.66 · So, b = c = 12.66 + 11 = 23.66
However, we know that these numbers are integers. So, c = b is not feasible·
a, b, and c are integers; a + b + c = 60; a ≤ b ≤ c; median is (a + 11)
Iteration 1: c = b
What is the least possible value of c?
· a + (a + 11) + (a + 11) = 60 · Or 3a = 38 or a = 12.66 · So, b = c = 12.66 + 11 = 23.66
However, we know that these numbers are integers. So, c = b is not feasible
a + (a + 11) + (a + 12) = 60 · Or 3a = 37 or a = 12.33.
·
The value of the numbers is not an integer in this scenario as well.
a, b, and c are integers; a + b + c = 60; a ≤ b ≤ c; median is (a + 11)
Iteration 1: c = b
Iteration 2: c = b + 1
So, c = (b + 1) is also not feasible·
· So, b = 23.33 and c = 24.33
NoteThe next lowest value possible for c is equating it to b + 1.
i.e., making ‘c’ just as little more than ‘b’ as possible
What is the least possible value of c?
Minimum Possible value of c = 25
Choice C.
· a + (a + 11) + (a + 13) = 60
· Or 3a = 36 or a = 12 · So, b = 23 and c = 25
Satisfies all conditions
a, b, and c are integers; a + b + c = 60; a ≤ b ≤ c; median is (a + 11)
Iteration 3: c = b + 2
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