Difference between revisions of "1985 AJHSME Problems"
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== Problem 22 == | == Problem 22 == | ||
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+ | Assume every 7-digit whole number is a possible telephone number except those that begin with <math>0</math> or <math>1</math>. What fraction of telephone numbers begin with <math>9</math> and end with <math>0</math>? | ||
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+ | <math>\text{(A)}\ \frac{1}{63} \qquad \text{(B)}\ \frac{1}{80} \qquad \text{(C)}\ \frac{1}{81} \qquad \text{(D)}\ \frac{1}{90} \qquad \text{(E)}\ \frac{1}{100}</math> | ||
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+ | ''Note: 0236230 is a valid 7-digit whole number for this problem (though not a telephone number), and all telephone numbers are 7-digit whole numbers.'' | ||
[[1985 AJHSME Problems/Problem 22|Solution]] | [[1985 AJHSME Problems/Problem 22|Solution]] |
Revision as of 19:51, 12 January 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
Problem 2
Problem 3
Problem 4
The area of polygon , in square units, is
Problem 5
Problem 6
A ream of paper containing sheets is
cm thick. Approximately how many sheets of this type of paper would there be in a stack
cm high?
Problem 7
A "stair-step" figure is made of alternating black and white squares in each row. Rows through
are shown. All rows being and end with a white square. The number of black squares in the
row is
Problem 8
If , the largest number in the set
is
Problem 9
The product of the 9 factors
Problem 10
The fraction halfway between and
(on the number line) is
Problem 11
A piece of paper containing six joined squares labeled as shown in the diagram is folded along the edges of the squares to form a cube. The label of the face opposite the face labeled is
Problem 12
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are ,
and
. The area of the square is
Problem 13
If you walk for minutes at a rate of
and then run for
minutes at a rate of
, how many miles will you have gone at the end of one hour and
minutes?
Problem 14
The difference between a sales tax and a
sales tax on an item priced at <dollar/>
before tax is
<dollar/>
<dollar/>
<dollar/>
<dollar/>
<dollar/>
Problem 15
How many whole numbers between and
contain the digit
?
Problem 16
The ratio of boys to girls in Mr. Brown's math class is . If there are
students in the class, how many more girls than boys are in the class?
Problem 17
If your average score on your first six mathematics tests was and your average score on your first seven mathematics tests was
, then your score on the seventh test was
Problem 18
Nine copies of a certain pamphlet cost less than <dollar/> while ten copies of the same pamphlet (at the same price) cost more than <dollar/>
. How much does one copy of this pamphlet cost?
<dollar/>
<dollar/>
<dollar/>
<dollar/>
<dollar/>
Problem 19
If the length and width of a rectangle are each increased by , then the perimeter of the rectangle is increased by
Problem 20
In a certain year, January had exactly four Tuesdays and four Saturdays. On what day did January fall that year?
Problem 21
Mr. Green receives a raise every year. His salary after four such raises has gone up by what percent?
Problem 22
Assume every 7-digit whole number is a possible telephone number except those that begin with or
. What fraction of telephone numbers begin with
and end with
?
Note: 0236230 is a valid 7-digit whole number for this problem (though not a telephone number), and all telephone numbers are 7-digit whole numbers.
Problem 23
Problem 24
Problem 25
Five cards are lying on a table as shown.
Each card has a letter on one side and a whole number on the other side. Jane said, "If a vowel is on one side of any card, then an even number is on the other side." Mary showed Jane was wrong by turning over one card. Which card did Mary turn over?