Aman verma wrote:Q: The average of a set of whole numbers is 27.2. When 20% of the elements(i.e Numbers) are eliminated from the set of numbers then the average becomes 34. The number of elements in the new set of Numbers can be :
a) 27
b) 35
c) 52
d) 63
e) 71
PS: Please solve this algebraically. This problem can be easily solved by plugging in the options, but solving this algebraically will clarify the underlying logic and the mechanics of the problem.
Let N = the number of elements and A = the average of elements.
Sum = N*A.
When old N decreases by 80%, new N = (4/5)N.
When old A increases from 27.2 to 34 -- an increase of 25% -- new A = (5/4)A.
Thus, new sum = (4/5)N * (5/4)A = N*A.
Thus, the new sum is equal to the old sum -- REGARDLESS of the number of elements.
Since the number of elements has no effect upon the sum, the only requirement is that the number of elements be a WHOLE NUMBER.
Since new N = (4/5)N, we know that N must be a multiple of 5 and that (4/5)N -- the new number of elements -- must be a multiple of 4.
To illustrate:
If old N=5, then new N = (4/5)N = 4.
If old N=10, then new N = (4/5)10 = 8.
If old N=15, then new N = (4/5)15 = 12.
In each case, new N is a multiple of 4.
Among the 5 answer choices, only 52 is a multiple of 4.
The correct answer is
C.
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