guerrero wrote:Five consecutive integers are labeled n1, n2, n3, n4, and n5. Which of these numbers should be removed, in order for the sum of the other four to become 4/5th of the original sum?
(A)n1
(B)n2
(C)n3
(D)n4
(E)n5
OA
C
Let the five integers be 1, 2, 3, 4, and 5.
Original sum = number*median = 5*3 = 15.
New sum = 4/5 of the original sum = (4/5)15 = 12.
Integer that must be removed = original sum - new sum = 15-12 = 3.
The correct answer is
C.
Algebraic solution:
Let the five integers be n, n+1, n+2, n+3, and n+4.
Original sum = number*median = 5(n+2) = 5n+10.
New sum = 4/5 of the original sum = (4/5)(5n+10)= 4n+8
Integer that must be removed = original sum - new sum = (5n+10) - (4n+8) = n+2, which is the value of the third integer.
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