Discussion
a,b,c,d and e are five consecutive numbers in increasing order of size. Deleting one number from the set decreased the sum of the remaining numbers in the set by 20%.
Which one of the following numbers was deleted?
Answer: C
Five consecutive numbers are symmetric about the middle one, so their total is five times that middle value. Writing the set as \( c-2,\, c-1,\, c,\, c+1,\, c+2 \):
\[ S = 5c \]
Removing one member cuts the total by 20 per cent, so the number removed is
\[ 0.20 \times 5c = c \]
which is the middle number, c.
The result holds whatever the five numbers are, since the arithmetic never uses their actual values - only that they are consecutive and so centred on \( c \).
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