Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1995 AJHSME Problems"
Line 41: Line 41:
 
Find the smallest whole number that is larger than the sum
 
Find the smallest whole number that is larger than the sum
  
−
<center>
+
<cmath>2\dfrac{1}{2}+3\dfrac{1}{3}+4\dfrac{1}{4}+5\dfrac{1}{5}.</cmath>
−
<math>2\dfrac{1}{2}+3\dfrac{1}{3}+4\dfrac{1}{4}+5\dfrac{1}{5}.</math>
 
−
</center>
 
  
 
<math>\text{(A)}\ 14 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 16 \qquad \text{(D)}\ 17 \qquad \text{(E)}\ 18</math>
 
<math>\text{(A)}\ 14 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 16 \qquad \text{(D)}\ 17 \qquad \text{(E)}\ 18</math>
Line 50: Line 48:
  
 
==Problem 6==
 
==Problem 6==
 +
 +
Figures <math>I</math>, <math>II</math>, and <math>III</math> are squares.  The perimeter of <math>I</math> is <math>12</math> and the perimeter of <math>II</math> is <math>24</math>.  The perimeter of <math>III</math> is
 +
 +
{{image}}
 +
 +
<math>\text{(A)}\ 9 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 72 \qquad \text{(D)}\ 81</math>
  
 
[[1995 AJHSME Problems/Problem 6|Solution]]
 
[[1995 AJHSME Problems/Problem 6|Solution]]
  
 
==Problem 7==
 
==Problem 7==
 +
 +
At Clover View Junior High, one half of the students go home on the school bus.  One fourth go home by automobile.  One tenth go home on their bicycles.  The rest walk home.  What fractional part of the students walk home?
 +
 +
<math>\text{(A)}\ \dfrac{1}{16} \qquad \text{(B)}\ \dfrac{3}{20} \qquad \text{(C)}\ \dfrac{1}{3} \qquad \text{(D)}\ \dfrac{17}{20} \qquad \text{(E)}\ \dfrac{9}{10}</math>
  
 
[[1995 AJHSME Problems/Problem 7|Solution]]
 
[[1995 AJHSME Problems/Problem 7|Solution]]
  
 
==Problem 8==
 
==Problem 8==
 +
 +
An American traveling in Italy wishes to exchange American money (dollars) for Italian money (lire).  If 3000 lire = <dollar/>1.60, how much lire will the traveler receive in exchange for <dollar/>1.00?
 +
 +
<math>\text{(A)}\ 180 \qquad \text{(B)}\ 480 \qquad \text{(C)}\ 1800 \qquad \text{(D)}\ 1875 \qquad \text{(E)}\ 4875</math>
  
 
[[1995 AJHSME Problems/Problem 8|Solution]]
 
[[1995 AJHSME Problems/Problem 8|Solution]]
  
 
==Problem 9==
 
==Problem 9==
 +
 +
Three congruent circles with centers <math>P</math>, <math>Q</math>, and <math>R</math> are tangent to the sides of rectangle <math>ABCD</math> as shown.  The circle centered at <math>Q</math> has diameter <math>4</math> and passes through points <math>P</math> and <math>R</math>.  The area of the rectangle is
 +
 +
{{image}}
 +
 +
<math>\text{(A)}\ 16 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 64 \qquad \text{(E)}\ 128</math>
  
 
[[1995 AJHSME Problems/Problem 9|Solution]]
 
[[1995 AJHSME Problems/Problem 9|Solution]]
  
 
==Problem 10==
 
==Problem 10==
 +
 +
A jacket and a shirt originally sold for <dollar/>80 and <dollar/>40, respectively.  During a sale Chris bought the <dollar/>80 jacket at a <math>40\%</math> discount and the <dollar/>40 shirt at a <math>55\%</math> discount.  The total amount saved was what percent of the total of the original prices?
 +
 +
<math>\text{(A)}\ 45\% \qquad \text{(B)}\ 47\dfrac{1}{2}\% \qquad \text{(C)}\ 50\% \qquad \text{(D)}\ 79\dfrac{1}{6}\% \qquad \text{(E)}\ 95\%</math>.
  
 
[[1995 AJHSME Problems/Problem 10|Solution]]
 
[[1995 AJHSME Problems/Problem 10|Solution]]

Revision as of 22:57, 9 August 2010

Problem 1

Walter has exactly one penny, one nickel, one dime and one quarter in his pocket. What percent of one dollar is in his pocket?

$\text{(A)}\ 4\% \qquad \text{(B)}\ 25\% \qquad \text{(C)}\ 40\% \qquad \text{(D)}\ 41\% \qquad \text{(E)}\ 59\%$

Solution

Problem 2

Jose is $4$ years younger than Zack. Zack is $3$ years older than Inez. Inez is $15$ years old. How old is Jose?

$\text{(A)}\ 8 \qquad \text{(B)}\ 11 \qquad \text{(C)}\ 14 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 22$

Solution

Problem 3

Which of the following operations has the same effect on a number as multiplying by $\dfrac{3}{4}$ and then dividing by $\dfrac{3}{5}$?

$\text{(A)}\ \text{dividing by }\dfrac{4}{3} \qquad \text{(B)}\ \text{dividing by }\dfrac{9}{20} \qquad \text{(C)}\ \text{multiplying by }\dfrac{9}{20} \qquad \text{(D)}\ \text{dividing by }\dfrac{5}{4} \qquad \text{(E)}\ \text{multiplying by }\dfrac{5}{4}$

Solution

Problem 4

A teacher tells the class,

"Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer."

Ben thinks of $6$, and gives his answer to Sue. What should Sue's answer be?

$\text{(A)}\ 18 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 26 \qquad \text{(D)}\ 27 \qquad \text{(E)}\ 30$

Solution

Problem 5

Find the smallest whole number that is larger than the sum

\[2\dfrac{1}{2}+3\dfrac{1}{3}+4\dfrac{1}{4}+5\dfrac{1}{5}.\]

$\text{(A)}\ 14 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 16 \qquad \text{(D)}\ 17 \qquad \text{(E)}\ 18$

Solution

Problem 6

Figures $I$, $II$, and $III$ are squares. The perimeter of $I$ is $12$ and the perimeter of $II$ is $24$. The perimeter of $III$ is

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

$\text{(A)}\ 9 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 72 \qquad \text{(D)}\ 81$

Solution

Problem 7

At Clover View Junior High, one half of the students go home on the school bus. One fourth go home by automobile. One tenth go home on their bicycles. The rest walk home. What fractional part of the students walk home?

$\text{(A)}\ \dfrac{1}{16} \qquad \text{(B)}\ \dfrac{3}{20} \qquad \text{(C)}\ \dfrac{1}{3} \qquad \text{(D)}\ \dfrac{17}{20} \qquad \text{(E)}\ \dfrac{9}{10}$

Solution

Problem 8

An American traveling in Italy wishes to exchange American money (dollars) for Italian money (lire). If 3000 lire = <dollar/>1.60, how much lire will the traveler receive in exchange for <dollar/>1.00?

$\text{(A)}\ 180 \qquad \text{(B)}\ 480 \qquad \text{(C)}\ 1800 \qquad \text{(D)}\ 1875 \qquad \text{(E)}\ 4875$

Solution

Problem 9

Three congruent circles with centers $P$, $Q$, and $R$ are tangent to the sides of rectangle $ABCD$ as shown. The circle centered at $Q$ has diameter $4$ and passes through points $P$ and $R$. The area of the rectangle is

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

$\text{(A)}\ 16 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 64 \qquad \text{(E)}\ 128$

Solution

Problem 10

A jacket and a shirt originally sold for <dollar/>80 and <dollar/>40, respectively. During a sale Chris bought the <dollar/>80 jacket at a $40\%$ discount and the <dollar/>40 shirt at a $55\%$ discount. The total amount saved was what percent of the total of the original prices?

$\text{(A)}\ 45\% \qquad \text{(B)}\ 47\dfrac{1}{2}\% \qquad \text{(C)}\ 50\% \qquad \text{(D)}\ 79\dfrac{1}{6}\% \qquad \text{(E)}\ 95\%$.

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

1995 AJHSME (Problems • Answer Key • Resources)
Preceded by
1994 AJHSME 		Followed by
1996 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
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1995_AJHSME_Problems&oldid=35606"