1995 AMC 8 Problem 3

Below is the professionally curated solution for Problem 3 of the 1995 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 8 solutions, or check the answer key.

Concepts:fraction

Difficulty rating: 560

Which of the following operations has the same effect on a number as multiplying by $\dfrac34$ and then dividing by $\dfrac35?$

dividing by $\dfrac43$

dividing by $\dfrac{9}{20}$

multiplying by $\dfrac{9}{20}$

dividing by $\dfrac54$

multiplying by $\dfrac54$

Dividing by $\dfrac35$ is the same as multiplying by $\dfrac53,$ so the two operations together multiply by

$\dfrac34 \times \dfrac53 = \dfrac54.$

So the combined effect is multiplying by $\dfrac54$ .

Thus, the correct answer is E .