1996 AMC 8 Problem 4 — Solution | LIVE by Po-Shen Loh

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1996 AMC 8 Problem 4

Attempt Problem 4 of the 1996 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 1996 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

4.

What is the value of the following expression?

$\frac{2 + 4 + 6 + \cdots + 34}{3 + 6 + 9 + \cdots + 51}$

$\dfrac{1}{3}$

$\dfrac{2}{3}$

$\dfrac{3}{2}$

$\dfrac{17}{3}$

$\dfrac{34}{3}$

Answer: B

Concepts:arithmetic sequence ratio and proportion

Difficulty rating: 800

Solution:

The numerator is $2(1 + 2 + \cdots + 17)$ and the denominator is $3(1 + 2 + \cdots + 17)$ .

The common factor cancels, leaving $\dfrac{2}{3}$ .

Thus, the correct answer is B .

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