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Difference between revisions of "1994 AJHSME Problems"
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== Problem 3 ==
 
== Problem 3 ==
 +
 +
Each day Maria must work <math>8</math> hours.  This does not include the <math>45</math> minutes she takes for lunch.  If she begins working at <math>\text{7:25 A.M.}</math> and takes her lunch break at noon, then her working day will end at
 +
 +
<math>\text{(A)}\ \text{3:40 P.M.} \qquad \text{(B)}\ \text{3:55 P.M.} \qquad \text{(C)}\ \text{4:10 P.M.} \qquad \text{(D)}\ \text{4:25 P.M.} \qquad \text{(E)}\ \text{4:40 P.M.}</math>
  
 
[[1994 AJHSME Problems/Problem 3|Solution]]
 
[[1994 AJHSME Problems/Problem 3|Solution]]
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== Problem 5 ==
 
== Problem 5 ==
 +
 +
Given that <math>\text{1 mile} = \text{8 furlongs}</math> and <math>\text{1 furlong} = \text{40 rods}</math>, the number of rods in one mile is
 +
 +
<math>\text{(A)}\ 5 \qquad \text{(B)}\ 320 \qquad \text{(C)}\ 660 \qquad \text{(D)}\ 1760 \qquad \text{(E)}\ 5280</math>
  
 
[[1994 AJHSME Problems/Problem 5|Solution]]
 
[[1994 AJHSME Problems/Problem 5|Solution]]
  
 
== Problem 6 ==
 
== Problem 6 ==
 +
 +
The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is
 +
 +
<math>\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8</math>
  
 
[[1994 AJHSME Problems/Problem 6|Solution]]
 
[[1994 AJHSME Problems/Problem 6|Solution]]
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== Problem 8 ==
 
== Problem 8 ==
 +
 +
For how many three-digit whole numbers does the sum of the digits equal <math>25</math>?
 +
 +
<math>\text{(A)}\ 2 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 10</math>
  
 
[[1994 AJHSME Problems/Problem 8|Solution]]
 
[[1994 AJHSME Problems/Problem 8|Solution]]
  
 
== Problem 9 ==
 
== Problem 9 ==
 +
 +
A shopper buys a <math>100</math> dollar coat on sale for <math>20\% </math> off.  An additional <math>5</math> dollars are taken off the sale price by using a discount coupon.  A sales tax of <math>8\% </math> is paid on the final selling price.  The total amount the shopper pays for the coat is
 +
 +
<math>\text{(A)}\ \text{81.00 dollars} \qquad \text{(B)}\ \text{81.40 dollars} \qquad \text{(C)}\ \text{82.00 dollars} \qquad \text{(D)}\ \text{82.08 dollars} \qquad \text{(E)}\ \text{82.40 dollars}</math>
  
 
[[1994 AJHSME Problems/Problem 9|Solution]]
 
[[1994 AJHSME Problems/Problem 9|Solution]]
  
 
== Problem 10 ==
 
== Problem 10 ==
 +
 +
For how many positive integer values of <math>N</math> is the expression <math>\dfrac{36}{N+2}</math> an integer?
 +
 +
<math>\text{(A)}\ 7 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12</math>
  
 
[[1994 AJHSME Problems/Problem 10|Solution]]
 
[[1994 AJHSME Problems/Problem 10|Solution]]
  
 
== Problem 11 ==
 
== Problem 11 ==
 +
 +
Last summer <math>100</math> students attended basketball camp.  Of those attending, <math>52</math> were boys and <math>48</math> were girls.  Also, <math>40</math> students were from Jonas Middle School and <math>60</math> were from Clay Middle School.  Twenty of the girls were from Jonas Middle School.  How many of the boys were from Clay Middle School?
 +
 +
<math>\text{(A)}\ 20 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 48 \qquad \text{(E)}\ 52</math>
  
 
[[1994 AJHSME Problems/Problem 11|Solution]]
 
[[1994 AJHSME Problems/Problem 11|Solution]]
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== Problem 13 ==
 
== Problem 13 ==
 +
 +
The number halfway between <math>\dfrac{1}{6}</math> and <math>\dfrac{1}{4}</math> is
 +
 +
<math>\text{(A)}\ \dfrac{1}{10} \qquad \text{(B)}\ \dfrac{1}{5} \qquad \text{(C)}\ \dfrac{5}{24} \qquad \text{(D)}\ \dfrac{7}{24} \qquad \text{(E)}\ \dfrac{5}{12}</math>
  
 
[[1994 AJHSME Problems/Problem 13|Solution]]
 
[[1994 AJHSME Problems/Problem 13|Solution]]
  
 
== Problem 14 ==
 
== Problem 14 ==
 +
 +
Two children at a time can play pairball.  For <math>90</math> minutes, with only two children playing at time, five children take turns so that each one plays the same amount of time.  The number of minutes each child plays is
 +
 +
<math>\text{(A)}\ 9 \qquad \text{(B)}\ 10 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 20 \qquad \text{(E)}\ 36</math>
  
 
[[1994 AJHSME Problems/Problem 14|Solution]]
 
[[1994 AJHSME Problems/Problem 14|Solution]]
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== Problem 16 ==
 
== Problem 16 ==
 +
 +
The perimeter of one square is <math>3</math> times the perimeter of another square.  The area of the larger square is how many times the area of the smaller square?
 +
 +
<math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 9</math>
  
 
[[1994 AJHSME Problems/Problem 16|Solution]]
 
[[1994 AJHSME Problems/Problem 16|Solution]]
  
 
== Problem 17 ==
 
== Problem 17 ==
 +
 +
Pauline Bunyan can shovel snow at the rate of <math>20</math> cubic yards for the first hour, <math>19</math> cubic yards for the second, <math>18</math> for the third, etc., always shoveling one cubic yard less per hour than the previous hour.  If her driveway is <math>4</math> yards wide, <math>10</math> yards long, and covered with snow <math>3</math> yards deep, then the number of hours it will take her to shovel it clean is closest to
 +
 +
<math>\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 12</math>
  
 
[[1994 AJHSME Problems/Problem 17|Solution]]
 
[[1994 AJHSME Problems/Problem 17|Solution]]
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== Problem 20 ==
 
== Problem 20 ==
 +
 +
Let <math>W,X,Y</math> and <math>Z</math> be four different digits selected from the set
 +
 +
<center><math>\{ 1,2,3,4,5,6,7,8,9\}.</math></center>
 +
 +
If the sum <math>\dfrac{W}{X} + \dfrac{Y}{Z}</math> is to be as small as possible, then <math>\dfrac{W}{X} + \dfrac{Y}{Z}</math> must equal
 +
 +
<math>\text{(A)}\ \dfrac{2}{17} \qquad \text{(B)}\ \dfrac{3}{17} \qquad \text{(C)}\ \dfrac{17}{72} \qquad \text{(D)}\ \dfrac{25}{72} \qquad \text{(E)}\ \dfrac{13}{36}</math>
  
 
[[1994 AJHSME Problems/Problem 20|Solution]]
 
[[1994 AJHSME Problems/Problem 20|Solution]]

Revision as of 17:59, 19 April 2010

Problem 1

Which of the following is the largest?

$\text{(A)}\ \dfrac{1}{3} \qquad \text{(B)}\ \dfrac{1}{4} \qquad \text{(C)}\ \dfrac{3}{8} \qquad \text{(D)}\ \dfrac{5}{12} \qquad \text{(E)}\ \dfrac{7}{24}$

Solution

Problem 2

$\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}+\dfrac{55}{10}=$

$\text{(A)}\ 4\dfrac{1}{2} \qquad \text{(B)}\ 6.4 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 11$

Solution

Problem 3

Each day Maria must work $8$ hours. This does not include the $45$ minutes she takes for lunch. If she begins working at $\text{7:25 A.M.}$ and takes her lunch break at noon, then her working day will end at

$\text{(A)}\ \text{3:40 P.M.} \qquad \text{(B)}\ \text{3:55 P.M.} \qquad \text{(C)}\ \text{4:10 P.M.} \qquad \text{(D)}\ \text{4:25 P.M.} \qquad \text{(E)}\ \text{4:40 P.M.}$

Solution

Problem 4

Solution

Problem 5

Given that $\text{1 mile} = \text{8 furlongs}$ and $\text{1 furlong} = \text{40 rods}$, the number of rods in one mile is

$\text{(A)}\ 5 \qquad \text{(B)}\ 320 \qquad \text{(C)}\ 660 \qquad \text{(D)}\ 1760 \qquad \text{(E)}\ 5280$

Solution

Problem 6

The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is

$\text{(A)}\ 0 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8$

Solution

Problem 7

Solution

Problem 8

For how many three-digit whole numbers does the sum of the digits equal $25$?

$\text{(A)}\ 2 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 8 \qquad \text{(E)}\ 10$

Solution

Problem 9

A shopper buys a $100$ dollar coat on sale for $20\%$ off. An additional $5$ dollars are taken off the sale price by using a discount coupon. A sales tax of $8\%$ is paid on the final selling price. The total amount the shopper pays for the coat is

$\text{(A)}\ \text{81.00 dollars} \qquad \text{(B)}\ \text{81.40 dollars} \qquad \text{(C)}\ \text{82.00 dollars} \qquad \text{(D)}\ \text{82.08 dollars} \qquad \text{(E)}\ \text{82.40 dollars}$

Solution

Problem 10

For how many positive integer values of $N$ is the expression $\dfrac{36}{N+2}$ an integer?

$\text{(A)}\ 7 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12$

Solution

Problem 11

Last summer $100$ students attended basketball camp. Of those attending, $52$ were boys and $48$ were girls. Also, $40$ students were from Jonas Middle School and $60$ were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School?

$\text{(A)}\ 20 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 48 \qquad \text{(E)}\ 52$

Solution

Problem 12

Solution

Problem 13

The number halfway between $\dfrac{1}{6}$ and $\dfrac{1}{4}$ is

$\text{(A)}\ \dfrac{1}{10} \qquad \text{(B)}\ \dfrac{1}{5} \qquad \text{(C)}\ \dfrac{5}{24} \qquad \text{(D)}\ \dfrac{7}{24} \qquad \text{(E)}\ \dfrac{5}{12}$

Solution

Problem 14

Two children at a time can play pairball. For $90$ minutes, with only two children playing at time, five children take turns so that each one plays the same amount of time. The number of minutes each child plays is

$\text{(A)}\ 9 \qquad \text{(B)}\ 10 \qquad \text{(C)}\ 18 \qquad \text{(D)}\ 20 \qquad \text{(E)}\ 36$

Solution

Problem 15

Solution

Problem 16

The perimeter of one square is $3$ times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 9$

Solution

Problem 17

Pauline Bunyan can shovel snow at the rate of $20$ cubic yards for the first hour, $19$ cubic yards for the second, $18$ for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is $4$ yards wide, $10$ yards long, and covered with snow $3$ yards deep, then the number of hours it will take her to shovel it clean is closest to

$\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 12$

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Let $W,X,Y$ and $Z$ be four different digits selected from the set

$\{ 1,2,3,4,5,6,7,8,9\}.$

If the sum $\dfrac{W}{X} + \dfrac{Y}{Z}$ is to be as small as possible, then $\dfrac{W}{X} + \dfrac{Y}{Z}$ must equal

$\text{(A)}\ \dfrac{2}{17} \qquad \text{(B)}\ \dfrac{3}{17} \qquad \text{(C)}\ \dfrac{17}{72} \qquad \text{(D)}\ \dfrac{25}{72} \qquad \text{(E)}\ \dfrac{13}{36}$

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

See also

1994 AJHSME (Problems • Answer Key • Resources)
Preceded by
1993 AJHSME 		Followed by
1995 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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