Difference between revisions of "1998 AJHSME Problems/Problem 5"
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| − | ==Problem | + | ==Problem== |
Which of the following numbers is largest? | Which of the following numbers is largest? | ||
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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== | + | ==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. | ||
| + | ==Solution 2== | ||
| + | |||
| + | 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. | ||
| + | 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 == | ||
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* [[AJHSME Problems and Solutions]] | * [[AJHSME Problems and Solutions]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 22:10, 13 January 2023
Contents
Problem
Which of the following numbers is largest?
Solution 1
Looking at the different answer choices, we have (up to 10 digits after the decimal)
: 
: 
: 
: 
: 
By inspection, we can see that 
is the largest number.
Solution 2
Looking at the fifth digit after the decimal of each, we find that choices , , and are eliminated.
Since has a non-zero sixth digit after the decimal, unlike , we conclude that is the largest number.
See also
| 1998 AJHSME (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
