Math Multiple Choice
If 0 < a < b < c < d < e in the equation above, then the greatest increase in S would result from adding 1 to the value of which variable?
- (A) a CORRECT ANSWER
- (B) b
- (C) c
- (D) d
- (E) e
Explanation:
When the denominator of a fraction is increased, the value of the fraction decreases. Therefore, adding 1 go b, d, or e will decrease the sum S. Increasing one of the numerators, either a or c, will increase S. Adding 1 to a changes 
to 
, thereby increasing S by 
. Adding 1 to c changes 
to 
, thereby increasing S by 
. Since b<d, then 
. Therefore, adding 1 to a will result in the greatest increase in S. The correct answer is (A).
(from the October 14, 1997 test)