1985 AHSME Problems
- 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 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 See also
If , then
In right with legs and , arcs of circles are drawn, one with center and radius , the other with center and radius . They intersect the hypotenuse at and . Then, has length:
A large bag of coins contains pennies, dimes, and quarters. There are twice as many dimes as pennies and three times as many quarters as dimes. An amount of money which could be in the bag is
Which terms must be removed from the sum
if the sum of the remaining terms is equal to ?
One student in a class of boys and girls is chosen to represent the class. Each student is equally likely to be chosen and the probability that a boy is chosen is of the probability that a girl is chosen. The ratio of the number of boys to the total number of boys and girls is
In some computer languages (such as APL), when there are no parentheses in an algebraic expression, the operations are grouped from left to right. Thus, in such languages means the same as in ordinary algebraic notation. If is evaluated in such a language, the result in ordinary algebraic notation would be
Let and be real numbers with and nonzero. The solution to is less than the solution to if and only if
The odd positive integers , are arranged into five columns continuing with the pattern shown on the right. Counting from the left, the column in which appears in is the
How many distinguishable rearrangements of the letters in CONTEST have both the vowels first? (For instance, OETCNST is one such arrangement but OTETSNC is not.)
Exactly three of the interior angles of a convex polygon are obtuse. What is the maximum number of sides of such a polygon?
If and are positive numbers such that and , then the value of is:
If and , then the value of is
Six bags of marbles contain and marbles, respectively. One bag contains chipped marbles only. The other bags contain no chipped marbles. Jane takes three of the bags and George takes two of the others. Only the bag of chipped marbles remains. If Jane gets twice as many marbles as George, how many chipped marbles are there?
Consider the graphs and , where is a positive constant and and are real variables. In how many points do the two graphs intersect?
A wooden cube with edge length units (where is an integer ) is painted black all over. By slices parallel to its faces, the cube is cut into smaller cubes each of unit length. If the number of smaller cubes with just one face painted black is equal to the number of smaller cubes completely free of paint, what is ?
How many integers satisfy the equation
If and , where , then which of the following is not correct?
A non-zero digit is chosen in such a way that the probability of choosing digit is . The probability that the digit is chosen is exactly the probability that the digit is chosen in the set
Find the least positive integer for which is a non-zero reducible fraction.
Consider a sequence defined by
and in general
What is the smallest value of for which is an integer?
In , we have and . What is ?
In their base representation, the integer consists of a sequence of eights and the integer consists of a sequence of fives. What is the sum of the digits of the base representation of ?
Let be the greatest integer less than or equal to . Then the number of real solutions to is
|1986 AHSME (Problems • Answer Key • Resources)|
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