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Difference between revisions of "1997 AJHSME Problems"

(Created page with '==Problem 1== <math>\dfrac{1}{10} + \dfrac{9}{100} + \dfrac{9}{1000} + \dfrac{7}{10000} = </math> <math>\text{(A)}\ 0.0026 \qquad \text{(B)}\ 0.0197 \qquad \text{(C)}\ 0.1997 \…')
 
Line 8: Line 8:
  
 
== Problem 2 ==
 
== Problem 2 ==
 +
 +
Ahn chooses a two-digit integer, subtracts it from 200, and doubles the result.  What is the largest number Ahn can get?
 +
 +
<math>\text{(A)}\ 200 \qquad \text{(B)}\ 202 \qquad \text{(C)}\ 220 \qquad \text{(D)}\ 380 \qquad \text{(E)}\ 398</math>
  
 
[[1997 AJHSME Problems/Problem 2|Solution]]
 
[[1997 AJHSME Problems/Problem 2|Solution]]
  
 
==Problem 3==
 
==Problem 3==
 +
 +
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>
  
 
[[1997 AJHSME Problems/Problem 3|Solution]]
 
[[1997 AJHSME Problems/Problem 3|Solution]]
  
 
==Problem 4==
 
==Problem 4==
 +
 +
Julie is preparing a speech for her class.  Her speech must last between one-half hour and three-quarters of an hour.  The ideal rate of speech is 150 words per minute.  If Julie speaks at the ideal rate, which of the following number of words would be an appropriate length for her speech?
 +
 +
<math>\text{(A)}\ 2250 \qquad \text{(B)}\ 3000 \qquad \text{(C)}\ 4200 \qquad \text{(D)}\ 4350 \qquad \text{(E)}\ 5650</math>
  
 
[[1997 AJHSME Problems/Problem 4|Solution]]
 
[[1997 AJHSME Problems/Problem 4|Solution]]
  
 
==Problem 5==
 
==Problem 5==
 +
 +
There are many two-digit multiples of 7, but only two of the multiples have a digit sum of 10.  The sum of these two multiples of 7 is
 +
 +
<math>\text{(A)}\ 119 \qquad \text{(B)}\ 126 \qquad \text{(C)}\ 140 \qquad \text{(D)}\ 175 \qquad \text{(E)}\ 189</math>
  
 
[[1997 AJHSME Problems/Problem 5|Solution]]
 
[[1997 AJHSME Problems/Problem 5|Solution]]
  
 
==Problem 6==
 
==Problem 6==
 +
 +
In the number <math>74982.1035</math> the value of the ''place'' occupied by the digit 9 is how many times as great as the value of the ''place'' occupied by the digit 3?
 +
 +
<math>\text{(A)}\ 1,000 \qquad \text{(B)}\ 10,000 \qquad \text{(C)}\ 100,000 \qquad \text{(D)}\ 1,000,000 \qquad \text{(E)}\ 10,000,000</math>
  
 
[[1997 AJHSME Problems/Problem 6|Solution]]
 
[[1997 AJHSME Problems/Problem 6|Solution]]
  
 
==Problem 7==
 
==Problem 7==
 +
 +
The area of the smallest square that will contain a circle of radius 4 is
 +
 +
<math>\text{(A)}\ 8 \qquad \text{(B)}\ 16 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 64 \qquad \text{(E)}\ 128</math>
  
 
[[1997 AJHSME Problems/Problem 7|Solution]]
 
[[1997 AJHSME Problems/Problem 7|Solution]]
  
 
==Problem 8==
 
==Problem 8==
 +
 +
Walter gets up at 6:30 a.m., catches the school bus at 7:30 a.m., has 6 classes that last 50 minutes each, has 30 minutes for lunch, and has 2 hours additional time at school.  He takes the bus home and arrives at 4:00 p.m.  How many minutes has he spent on the bus?
 +
 +
<math>\text{(A)}\ 30 \qquad \text{(B)}\ 60 \qquad \text{(C)}\ 75 \qquad \text{(D)}\ 90 \qquad \text{(E)}\ 120</math>
  
 
[[1997 AJHSME Problems/Problem 8|Solution]]
 
[[1997 AJHSME Problems/Problem 8|Solution]]
  
 
==Problem 9==
 
==Problem 9==
 +
 +
Three students, with different names, line up single file.  What is the probability that they are in alphabetical order from front-to-back?
 +
 +
<math>\text{(A)}\ \dfrac{1}{12} \qquad \text{(B)}\ \dfrac{1}{9} \qquad \text{(C)}\ \dfrac{1}{6} \qquad \text{(D)}\ \dfrac{1}{3} \qquad \text{(E)}\ \dfrac{2}{3}</math>
  
 
[[1997 AJHSME Problems/Problem 9|Solution]]
 
[[1997 AJHSME Problems/Problem 9|Solution]]

Revision as of 23:52, 4 December 2010

Problem 1

$\dfrac{1}{10} + \dfrac{9}{100} + \dfrac{9}{1000} + \dfrac{7}{10000} =$

$\text{(A)}\ 0.0026 \qquad \text{(B)}\ 0.0197 \qquad \text{(C)}\ 0.1997 \qquad \text{(D)}\ 0.26 \qquad \text{(E)}\ 1.997$

Solution

Problem 2

Ahn chooses a two-digit integer, subtracts it from 200, and doubles the result. What is the largest number Ahn can get?

$\text{(A)}\ 200 \qquad \text{(B)}\ 202 \qquad \text{(C)}\ 220 \qquad \text{(D)}\ 380 \qquad \text{(E)}\ 398$

Solution

Problem 3

Which of the following numbers is the largest?

$\text{(A)}\ 0.97 \qquad \text{(B)}\ 0.979 \qquad \text{(C)}\ 0.9709 \qquad \text{(D)}\ 0.907 \qquad \text{(E)}\ 0.9089$

Solution

Problem 4

Julie is preparing a speech for her class. Her speech must last between one-half hour and three-quarters of an hour. The ideal rate of speech is 150 words per minute. If Julie speaks at the ideal rate, which of the following number of words would be an appropriate length for her speech?

$\text{(A)}\ 2250 \qquad \text{(B)}\ 3000 \qquad \text{(C)}\ 4200 \qquad \text{(D)}\ 4350 \qquad \text{(E)}\ 5650$

Solution

Problem 5

There are many two-digit multiples of 7, but only two of the multiples have a digit sum of 10. The sum of these two multiples of 7 is

$\text{(A)}\ 119 \qquad \text{(B)}\ 126 \qquad \text{(C)}\ 140 \qquad \text{(D)}\ 175 \qquad \text{(E)}\ 189$

Solution

Problem 6

In the number $74982.1035$ the value of the place occupied by the digit 9 is how many times as great as the value of the place occupied by the digit 3?

$\text{(A)}\ 1,000 \qquad \text{(B)}\ 10,000 \qquad \text{(C)}\ 100,000 \qquad \text{(D)}\ 1,000,000 \qquad \text{(E)}\ 10,000,000$

Solution

Problem 7

The area of the smallest square that will contain a circle of radius 4 is

$\text{(A)}\ 8 \qquad \text{(B)}\ 16 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 64 \qquad \text{(E)}\ 128$

Solution

Problem 8

Walter gets up at 6:30 a.m., catches the school bus at 7:30 a.m., has 6 classes that last 50 minutes each, has 30 minutes for lunch, and has 2 hours additional time at school. He takes the bus home and arrives at 4:00 p.m. How many minutes has he spent on the bus?

$\text{(A)}\ 30 \qquad \text{(B)}\ 60 \qquad \text{(C)}\ 75 \qquad \text{(D)}\ 90 \qquad \text{(E)}\ 120$

Solution

Problem 9

Three students, with different names, line up single file. What is the probability that they are in alphabetical order from front-to-back?

$\text{(A)}\ \dfrac{1}{12} \qquad \text{(B)}\ \dfrac{1}{9} \qquad \text{(C)}\ \dfrac{1}{6} \qquad \text{(D)}\ \dfrac{1}{3} \qquad \text{(E)}\ \dfrac{2}{3}$

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

See also

1997 AJHSME (Problems • Answer Key • Resources)
Preceded by
1996 AJHSME 		Followed by
1998 AJHSME
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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