Difference between revisions of "1997 AJHSME Problems/Problem 3"
Bluecarneal (talk | contribs) m (Created page with "Using a process of elimination: Tenths digit: All are equal Hundreths digit: A, B, and C all have hundreths digits greater than D and E. Thousandths digit: B has the largest ...") |
|||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
| − | Using | + | ==Problem== |
| + | |||
| + | Which of the following numbers is the largest? | ||
| + | |||
| + | <math>\text{(A)}\ 0.97 \qquad \text{(B)}\ 0.979 \qquad \text{(C)}\ 0.9709 \qquad \text{(D)}\ 0.907 \qquad \text{(E)}\ 0.9089</math> | ||
| + | |||
| + | |||
| + | ==Solution== | ||
| + | Using the process of elimination: | ||
Tenths digit: | Tenths digit: | ||
| − | All are equal | + | All tenths digits are equal, at <math>9</math>. |
Hundreths digit: | Hundreths digit: | ||
| − | A, B, and C all have hundreths | + | <math>A</math>, <math>B</math>, and <math>C</math> all have the same hundreths digit of <math>7</math>, and it is greater than the hundredths of <math>D</math> or <math>E</math> (which is <math>0</math>). Eliminate both <math>D</math> and <math>E</math>. |
Thousandths digit: | Thousandths digit: | ||
| − | B has the largest thousandths digit of | + | <math>B</math> has the largest thousandths digit of the remaining answers, and is the correct answer. <math>A</math> has an "invisible" thousandths digit of <math>0</math>, while <math>C</math> also has a thousdandths digit of <math>0</math>. |
<math>\boxed{\textbf{(B)}}</math> | <math>\boxed{\textbf{(B)}}</math> | ||
| + | |||
| + | == See also == | ||
| + | {{AJHSME box|year=1997|num-b=2|num-a=4}} | ||
| + | * [[AJHSME]] | ||
| + | * [[AJHSME Problems and Solutions]] | ||
| + | * [[Mathematics competition resources]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:26, 4 July 2013
Problem
Which of the following numbers is the largest?
Solution
Using the process of elimination:
Tenths digit:
All tenths digits are equal, at 
.
Hundreths digit:
, 
, and 
all have the same hundreths digit of 
, and it is greater than the hundredths of 
or 
(which is 
). Eliminate both and .
Thousandths digit:
has the largest thousandths digit of the remaining answers, and is the correct answer. has an "invisible" thousandths digit of , while also has a thousdandths digit of .
See also
| 1997 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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. 
