1998 AMC 8 Problem 10

Attempt Problem 10 of the 1998 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1998 AMC 8 solutions, or check the answer key.

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10.

Each of the letters $W,$ $X,$ $Y,$ and $Z$ represents a different integer in the set $\{ 1,2,3,4\},$ but not necessarily in that order. If $\dfrac{W}{X} - \dfrac{Y}{Z}=1,$ then the sum of $W$ and $Y$ is:

$3$

$4$

$5$

$6$

$7$

Answer: E

Concepts:fraction casework

Difficulty rating: 1070

Solution:

The only way to get a difference of $1$ is

$\frac31-\frac42=1.$

Thus $W=3$ and $Y=4$ , so $W+Y=7$ .

Thus, the correct answer is E .

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