1998 AJHSME Problems/Problem 5

Problem

Which of the following numbers is largest?

$\text{(A)}\ 9.12344 \qquad \text{(B)}\ 9.123\overline{4} \qquad \text{(C)}\ 9.12\overline{34} \qquad \text{(D)}\ 9.1\overline{234} \qquad \text{(E)}\ 9.\overline{1234}$

Solution 1

Looking at the different answer choices, we have (up to 10 digits after the decimal)

$A$ : $9.1234400000$

$B$ : $9.1234444444$

$C$ : $9.1234343434$

$D$ : $9.1234234234$

$E$ : $9.1234123412$

By inspection, we can see that $\boxed{B}$ is the largest number.

Solution 2

Looking at the fifth digit after the decimal of each, we find that choices $C$ , $D$ , and $E$ are eliminated. Since $B$ has a non-zero sixth digit after the decimal, unlike $A$ , we conclude that $\boxed{B}$ is the largest number.

1998 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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1998 AJHSME Problems/Problem 5

Contents

Problem

Solution 1

Solution 2

See also