Difference between revisions of "1998 AJHSME Problems/Problem 5"

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<math>\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}</math>
 
<math>\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}</math>
  
==Solution==
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==Solution 1==
  
 
Looking at the different answer choices, we have (up to 10 digits after the decimal)
 
Looking at the different answer choices, we have (up to 10 digits after the decimal)
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By inspection, we can see that <math>\boxed{B}</math> is the largest number.
 
By inspection, we can see that <math>\boxed{B}</math> is the largest number.
  
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==Solution 2==
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Looking at the fifth digit after the decimal of each, we find that choices <math>C</math>, <math>D</math>, and <math>E</math> are eliminated.
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Since <math>B</math> has a non-zero sixth digit after the decimal, unlike <math>A</math>, we conclude that <math>\boxed{B}</math> is the largest number.
  
 
== See also ==
 
== See also ==

Latest revision as of 21:10, 13 January 2023

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.

See also

1998 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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