Difference between revisions of "1990 AJHSME Problems"

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== Problem 12 ==
 
== Problem 12 ==
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There are twenty-four <math>4</math>-digit numbers that use each of the four digits <math>2</math>, <math>4</math>, <math>5</math>, and <math>7</math> exactly once.  Listed in numerical order from smallest to largest, the number in the <math>17\text{th}</math> position in the list is
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<math>\text{(A)}\ 4527 \qquad \text{(B)}\ 5724 \qquad \text{(C)}\ 5742 \qquad \text{(D)}\ 7245 \qquad \text{(E)}\ 7524</math>
  
 
[[1990 AJHSME Problems/Problem 12|Solution]]
 
[[1990 AJHSME Problems/Problem 12|Solution]]
  
 
== Problem 13 ==
 
== Problem 13 ==
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One proposal for new postage rates for a letter was <math>30</math> cents for the first ounce and <math>22</math> cents for each additional ounce (or fraction of an ounce).  The postage for a letter weighing <math>4.5</math> ounces was
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<math>\text{(A)}\ \text{96 cents} \qquad \text{(B)}\ \text{1.07 dollars} \qquad \text{(C)}\ \text{1.18 dollars} \qquad \text{(D)}\ \text{1.20 dollars} \qquad \text{(E)}\ \text{1.40 dollars}</math>
  
 
[[1990 AJHSME Problems/Problem 13|Solution]]
 
[[1990 AJHSME Problems/Problem 13|Solution]]
  
 
== Problem 14 ==
 
== Problem 14 ==
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A bag contains only blue balls and green balls.  There are <math>6</math> blue balls.  If the probability of drawing a blue ball at random from this bag is <math>\frac{1}{4}</math>, then the number of green balls in the bag is
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<math>\text{(A)}\ 12 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 24 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 36</math>
  
 
[[1990 AJHSME Problems/Problem 14|Solution]]
 
[[1990 AJHSME Problems/Problem 14|Solution]]
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== Problem 16 ==
 
== Problem 16 ==
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<math>1990-1980+1970-1960+\cdots -20+10 =</math>
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<math>\text{(A)}\ -990 \qquad \text{(B)}\ -10 \qquad \text{(C)}\ 990 \qquad \text{(D)}\ 1000 \qquad \text{(E)}\ 1990</math>
  
 
[[1990 AJHSME Problems/Problem 16|Solution]]
 
[[1990 AJHSME Problems/Problem 16|Solution]]
  
 
== Problem 17 ==
 
== Problem 17 ==
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A straight concrete sidewalk is to be <math>3</math> feet wide, <math>60</math> feet long, and <math>3</math> '''inches''' thick.  How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?
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<math>\text{(A)}\ 2 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 12 \qquad \text{(D)}\ 20 \qquad \text{(E)}\ \text{more than 20}</math>
  
 
[[1990 AJHSME Problems/Problem 17|Solution]]
 
[[1990 AJHSME Problems/Problem 17|Solution]]
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== Problem 19 ==
 
== Problem 19 ==
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There are <math>120</math> seats in a row.  What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?
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<math>\text{(A)}\ 30 \qquad \text{(B)}\ 40 \qquad \text{(C)}\ 41 \qquad \text{(D)}\ 60 \qquad \text{(E)}\ 119</math>
  
 
[[1990 AJHSME Problems/Problem 19|Solution]]
 
[[1990 AJHSME Problems/Problem 19|Solution]]
  
 
== Problem 20 ==
 
== Problem 20 ==
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The annual incomes of <math>1,000</math> families range from <math>8200</math> dollars to <math>98,000</math> dollars.  In error, the largest income was entered on the computer as <math>980,000</math> dollars.  The difference between the mean of the incorrect data and the mean of the actual data is
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<math>\text{(A)}\ \text{882 dollars} \qquad \text{(B)}\ \text{980 dollars} \qquad \text{(C)}\ \text{1078 dollars} \qquad \text{(D)}\ \text{482,000 dollars} \qquad \text{(E)}\ \text{882,000 dollars}</math>
  
 
[[1990 AJHSME Problems/Problem 20|Solution]]
 
[[1990 AJHSME Problems/Problem 20|Solution]]

Revision as of 22:24, 5 June 2009

Problem 1

Solution

Problem 2

Which digit of $.12345$, when changed to $9$, gives the largest number?

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 5$

Solution

Problem 3

Solution

Problem 4

Which of the following could not be the unit's digit [one's digit] of the square of a whole number?

$\text{(A)}\ 1 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8$

Solution

Problem 5

Which of the following is closest to the product $(.48017)(.48017)(.48017)$?

$\text{(A)}\ 0.011 \qquad \text{(B)}\ 0.110 \qquad \text{(C)}\ 1.10 \qquad \text{(D)}\ 11.0 \qquad \text{(E)}\ 110$

Solution

Problem 6

Which of these five numbers is the largest?

$\text{(A)}\ 13579+\frac{1}{2468} \qquad \text{(B)}\ 13579-\frac{1}{2468} \qquad \text{(C)}\ 13579\times \frac{1}{2468}$

$\text{(D)}\ 13579\div \frac{1}{2468} \qquad \text{(E)}\ 13579.2468$

Solution

Problem 7

When three different numbers from the set $\{ -3, -2, -1, 4, 5 \}$ are multiplied, the largest possible product is

$\text{(A)}\ 10 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 40 \qquad \text{(E)}\ 60$

Solution

Problem 8

A dress originally priced at $80$ dollars was put on sale for $25\%$ off. If $10\%$ tax was added to the sale price, then the total selling price (in dollars) of the dress was

$\text{(A)}\ \text{45 dollars} \qquad \text{(B)}\ \text{52 dollars} \qquad \text{(C)}\ \text{54 dollars} \qquad \text{(D)}\ \text{66 dollars} \qquad \text{(E)}\ \text{68 dollars}$

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

There are twenty-four $4$-digit numbers that use each of the four digits $2$, $4$, $5$, and $7$ exactly once. Listed in numerical order from smallest to largest, the number in the $17\text{th}$ position in the list is

$\text{(A)}\ 4527 \qquad \text{(B)}\ 5724 \qquad \text{(C)}\ 5742 \qquad \text{(D)}\ 7245 \qquad \text{(E)}\ 7524$

Solution

Problem 13

One proposal for new postage rates for a letter was $30$ cents for the first ounce and $22$ cents for each additional ounce (or fraction of an ounce). The postage for a letter weighing $4.5$ ounces was

$\text{(A)}\ \text{96 cents} \qquad \text{(B)}\ \text{1.07 dollars} \qquad \text{(C)}\ \text{1.18 dollars} \qquad \text{(D)}\ \text{1.20 dollars} \qquad \text{(E)}\ \text{1.40 dollars}$

Solution

Problem 14

A bag contains only blue balls and green balls. There are $6$ blue balls. If the probability of drawing a blue ball at random from this bag is $\frac{1}{4}$, then the number of green balls in the bag is

$\text{(A)}\ 12 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 24 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 36$

Solution

Problem 15

Solution

Problem 16

$1990-1980+1970-1960+\cdots -20+10 =$

$\text{(A)}\ -990 \qquad \text{(B)}\ -10 \qquad \text{(C)}\ 990 \qquad \text{(D)}\ 1000 \qquad \text{(E)}\ 1990$

Solution

Problem 17

A straight concrete sidewalk is to be $3$ feet wide, $60$ feet long, and $3$ inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?

$\text{(A)}\ 2 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 12 \qquad \text{(D)}\ 20 \qquad \text{(E)}\ \text{more than 20}$

Solution

Problem 18

Solution

Problem 19

There are $120$ seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?

$\text{(A)}\ 30 \qquad \text{(B)}\ 40 \qquad \text{(C)}\ 41 \qquad \text{(D)}\ 60 \qquad \text{(E)}\ 119$

Solution

Problem 20

The annual incomes of $1,000$ families range from $8200$ dollars to $98,000$ dollars. In error, the largest income was entered on the computer as $980,000$ dollars. The difference between the mean of the incorrect data and the mean of the actual data is

$\text{(A)}\ \text{882 dollars} \qquad \text{(B)}\ \text{980 dollars} \qquad \text{(C)}\ \text{1078 dollars} \qquad \text{(D)}\ \text{482,000 dollars} \qquad \text{(E)}\ \text{882,000 dollars}$

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

See also

1990 AJHSME (ProblemsAnswer KeyResources)
Preceded by
1989 AJHSME
Followed by
1991 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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