Difference between revisions of "1995 AHSME Problems"
(Problems 23 and 22... Could someone take over problems while I *try to* post solutions?) |
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== Problem 20 == | == Problem 20 == | ||
+ | If <math>a,b</math> and <math>c</math> are three (not necessarily different) numbers chosen randomly and with replacement from the set <math>\{1,2,3,4,5 \}</math>, the probability that <math>ab + c</math> is even is | ||
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+ | <math> \mathrm{(A) \ \frac {2}{5} } \qquad \mathrm{(B) \ \frac {59}{125} } \qquad \mathrm{(C) \ \frac {1}{2} } \qquad \mathrm{(D) \ \frac {64}{125} } \qquad \mathrm{(E) \ \frac {3}{5} } </math> | ||
[[1995 AMC 12 Problems/Problem 20|Solution]] | [[1995 AMC 12 Problems/Problem 20|Solution]] |
Revision as of 11:32, 8 January 2008
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 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 See also
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
If and
are three (not necessarily different) numbers chosen randomly and with replacement from the set
, the probability that
is even is
Problem 21
Problem 22
A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have lengths 13,19,20,25 and 31, although this is not necessarily their order around the pentagon. The area of the pentagon is
Problem 23
The sides of a triangle have lengths 11,15, and , where
is an integer. For how many values of
is the triangle obtuse?
Problem 24
There exist positive integers and
, with no common factor greater than 1, such that
What is ?
Problem 25
A list of five positive integers has mean 12 and range 18. The mode and median are both 8. How many different values are possible for the second largest element of the list?
Problem 26
In the figure, and
are diameters of the circle with center
,
, and chord
intersects
at
. If
and
, then the area of the circle is
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
Link: http://www.artofproblemsolving.com/Forum/viewtopic.php?t=62477
Problem 27
Consider the triangular array of numbers with 0,1,2,3,... along the sides and interior numbers obtained by adding the two adjacent numbers in the previous row. Rows 1 through 6 are shown.
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
A table really needs to go there... Link: http://www.artofproblemsolving.com/Forum/viewtopic.php?search_id=1526011879&t=62471
Let denote the sum of the numbers in row
. What is the remainder when
is divided by 100?
Problem 28
Two parallel chords in a circle have lengths 10 and 14, and the distance between them is 6. The chord parallel to these chords and midway between them is of length where
is
Problem 29
For how many three-element sets of positive integers is it true that
?
Problem 30
A large cube is formed by stacking 27 unit cubes. A plane is perpendicular to one of the internal diagonals of the large cube and bisects that diagonal. The number of unit cubes that the plane intersects is