Difference between revisions of "1990 AJHSME Problems"
5849206328x (talk | contribs) |
5849206328x (talk | contribs) |
||
Line 1: | Line 1: | ||
==Problem 1== | ==Problem 1== | ||
+ | |||
+ | What is the smallest sum of two <math>3</math>-digit numbers that can be obtained by placing each of the six digits <math>4,5,6,7,8,9</math> in one of the six boxes in this addition problem? | ||
+ | |||
+ | <asy> | ||
+ | unitsize(12); | ||
+ | draw((0,0)--(10,0)); draw((-1.5,1.5)--(-1.5,2.5)); draw((-1,2)--(-2,2)); | ||
+ | draw((1,1)--(3,1)--(3,3)--(1,3)--cycle); draw((1,4)--(3,4)--(3,6)--(1,6)--cycle); | ||
+ | draw((4,1)--(6,1)--(6,3)--(4,3)--cycle); draw((4,4)--(6,4)--(6,6)--(4,6)--cycle); | ||
+ | draw((7,1)--(9,1)--(9,3)--(7,3)--cycle); draw((7,4)--(9,4)--(9,6)--(7,6)--cycle); | ||
+ | </asy> | ||
+ | |||
+ | <math>\text{(A)}\ 947 \qquad \text{(B)}\ 1037 \qquad \text{(C)}\ 1047 \qquad \text{(D)}\ 1056 \qquad \text{(E)}\ 1245</math> | ||
[[1990 AJHSME Problems/Problem 1|Solution]] | [[1990 AJHSME Problems/Problem 1|Solution]] | ||
Line 12: | Line 24: | ||
== Problem 3 == | == Problem 3 == | ||
+ | |||
+ | What fraction of the square is shaded? | ||
+ | |||
+ | <asy> | ||
+ | draw((0,0)--(0,3)--(3,3)--(3,0)--cycle); | ||
+ | draw((0,2)--(2,2)--(2,0)); draw((0,1)--(1,1)--(1,0)); draw((0,0)--(3,3)); | ||
+ | fill((0,0)--(0,1)--(1,1)--cycle,grey); | ||
+ | fill((1,0)--(1,1)--(2,2)--(2,0)--cycle,grey); | ||
+ | fill((0,2)--(2,2)--(3,3)--(0,3)--cycle,grey); | ||
+ | </asy> | ||
+ | |||
+ | <math>\text{(A)}\ \frac{1}{3} \qquad \text{(B)}\ \frac{2}{5} \qquad \text{(C)}\ \frac{5}{12} \qquad \text{(D)}\ \frac{3}{7} \qquad \text{(E)}\ \frac{1}{2}</math> | ||
[[1990 AJHSME Problems/Problem 3|Solution]] | [[1990 AJHSME Problems/Problem 3|Solution]] | ||
Line 58: | Line 82: | ||
== Problem 9 == | == Problem 9 == | ||
+ | |||
+ | The grading scale shown is used at Jones Junior High. The fifteen scores in Mr. Freeman's class were: <cmath>\begin{tabular}[t]{lllllllll} | ||
+ | 89, & 72, & 54, & 97, & 77, & 92, & 85, & 74, & 75, \\ | ||
+ | 63, & 84, & 78, & 71, & 80, & 90. & & & \\ | ||
+ | \end{tabular}</cmath> | ||
+ | |||
+ | In Mr. Freeman's class, what percent of the students received a grade of C? | ||
+ | |||
+ | <cmath>\boxed{\begin{tabular}[t]{cc} | ||
+ | A: & 93 - 100 \\ | ||
+ | B: & 85 - 92 \\ | ||
+ | C: & 75 - 84 \\ | ||
+ | D: & 70 - 74 \\ | ||
+ | F: & 0 - 69 | ||
+ | \end{tabular}}</cmath> | ||
+ | |||
+ | <math>\text{(A)}\ 20\% \qquad \text{(B)}\ 25\% \qquad \text{(C)}\ 30\% \qquad \text{(D)}\ 33\frac{1}{3}\% \qquad \text{(E)}\ 40\% </math> | ||
[[1990 AJHSME Problems/Problem 9|Solution]] | [[1990 AJHSME Problems/Problem 9|Solution]] |
Revision as of 20:54, 20 June 2009
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
What is the smallest sum of two -digit numbers that can be obtained by placing each of the six digits in one of the six boxes in this addition problem?
Problem 2
Which digit of , when changed to , gives the largest number?
Problem 3
What fraction of the square is shaded?
Problem 4
Which of the following could not be the unit's digit [one's digit] of the square of a whole number?
Problem 5
Which of the following is closest to the product ?
Problem 6
Which of these five numbers is the largest?
Problem 7
When three different numbers from the set are multiplied, the largest possible product is
Problem 8
A dress originally priced at dollars was put on sale for off. If tax was added to the sale price, then the total selling price (in dollars) of the dress was
Problem 9
The grading scale shown is used at Jones Junior High. The fifteen scores in Mr. Freeman's class were:
In Mr. Freeman's class, what percent of the students received a grade of C?
Problem 10
Problem 11
Problem 12
There are twenty-four -digit numbers that use each of the four digits , , , and exactly once. Listed in numerical order from smallest to largest, the number in the position in the list is
Problem 13
One proposal for new postage rates for a letter was cents for the first ounce and cents for each additional ounce (or fraction of an ounce). The postage for a letter weighing ounces was
Problem 14
A bag contains only blue balls and green balls. There are blue balls. If the probability of drawing a blue ball at random from this bag is , then the number of green balls in the bag is
Problem 15
Problem 16
Problem 17
A straight concrete sidewalk is to be feet wide, feet long, and 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?
Problem 18
Problem 19
There are 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?
Problem 20
The annual incomes of families range from dollars to dollars. In error, the largest income was entered on the computer as dollars. The difference between the mean of the incorrect data and the mean of the actual data is
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
See also
1990 AJHSME (Problems • Answer Key • Resources) | ||
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 |