# 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)
CORRECT ANSWER*a* - (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)