1996 AMC 8 Problem 11 — Solution | LIVE by Po-Shen Loh

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1996 AMC 8 Problem 11

Below is the professionally curated solution for Problem 11 of the 1996 AMC 8, 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 of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:estimation

Difficulty rating: 860

11.

Let $x$ be the number

$0.\underbrace{0000\ldots00001}_{1996 \text{ zeros}},$

where there are $1996$ zeros after the decimal point. Which of the following expressions represents the largest number?

$3 + x$

$3 - x$

$3 \cdot x$

$3 / x$

$x / 3$

Solution:

Since $x$ is a very small positive number, $3 + x$ and $3 - x$ are near $3$ , while $3 \cdot x$ and $x / 3$ are near $0$ .

But $3 / x$ is $3$ followed by $1997$ zeros, far larger than any other choice.

Thus, the correct answer is D .

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