Louis14 wrote:
Given the numbers 1/8, 1/5, 2/3, -1/4, and 1/120, if one more number is added to the group and the average increases by 1/20, what is the value of that number?
(A) 1/20
(B) 1/5
(C) 1/4
(D) 3/8
(E) 9/20
Method 1: Sum of the 5 numbers = 1/8 + 1/5 + 2/3 - 1/4 + 1/120 = (15 + 24 + 80 - 30 + 1)/120 = 3/4
Mean of the 5 numbers = 3/(4*5) = 3/20
Assuming the number as n, since the average increases by 1/20, we have:
\((3/4 + n)/6 = 3/20 + 1/20\)
\(=> 3/4 + n = 24/20\)
\(=> n = 9/20\)
\(Method 2:\) Can be used in case you have very little time to solve out the actual answer - This is what is called an
educated guess:
The group has 5 numbers
On adding the new number, the average increases by 1/20
=> The value of each of the initial 5 numbers has increased by 1/20
=> The sum of the initial 5 numbers has increased by 5 * 1/20 = 5/20
This extra
5/20 must have come from the new 6th number when the numbers were averaged out.
Thus, this new number must be greater than 5/20 (or 1/4) - this rules out Options A, B, C
[Now, you can say that Option D (= 3/8) looks odd since it is pretty close to 1/4; hence, we go along with E.]
However, let's keep solving:
The mean of the 5 numbers initially = 3/20
Thus, the final value of the mean = 3/20 + 1/20 =
4/20 -- this would have been the value of the 6th term as well after averaging out
Thus, the actual value of the 6th term =
5/20 +
4/20 = 9/20
Answer E _________________
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