Question

If the product $\dfrac{3}{2}\cdot \dfrac{4}{3}\cdot \dfrac{5}{4}\cdot \dfrac{6}{5}\cdot \ldots\cdot \dfrac{a}{b} = 9,$ what is the sum of $a$ and $b?$

$11$

$13$

$17$

$35$

$37$

Answer: D

Concepts:telescoping fraction

Difficulty rating: 1340

Solution:

Note that the numerator of each fraction cancels with the denominator of the fraction to its right.

We can then cancel out all these terms to get a final equation of $\dfrac{a}{2} = 9 \Rightarrow a = 18 \Rightarrow b = 17.$

The desired sum is then $18 + 17 = 35.$

Thus, D is the correct answer.

1997 AMC 8 Problem 19

Answer: D

Difficulty rating: 1340

Solution:

Problem 19 in Other Years