Difference between revisions of "1996 AHSME Problems"
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==Problem 16== | ==Problem 16== | ||
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+ | A fair standard six-sided dice is tossed three times. Given that the sum of the first two tosses equal the third, what is the probability that at least one "2" is tossed? | ||
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+ | <math> \text{(A)}\ \frac{1}{6}\qquad\text{(B)}\ \frac{91}{216}\qquad\text{(C)}\ \frac{1}{2}\qquad\text{(D)}\ \frac{8}{15}\qquad\text{(E)}\ \frac{7}{12} </math> | ||
[[1996 AHSME Problems/Problem 16|Solution]] | [[1996 AHSME Problems/Problem 16|Solution]] |
Revision as of 11:08, 19 August 2011
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
Problem 1
The addition below is incorrect. What is the largest digit that can be changed to make the addition correct?
$\begin{tabular}{r}&\ \texttt{6 4 1}\\ \texttt{8 5 2} &+\texttt{9 7 3}\\ \hline \texttt{2 4 5 6}\end{tabular}$ (Error compiling LaTeX. Unknown error_msg)
Problem 2
Each day Walter gets dollars for doing his chores or
dollars for doing them exceptionally well. After
days of doing his chores daily, Walter has received a total of
dollars. On how many days did Walter do them exceptionally well?
Problem 3
Problem 4
Six numbers from a list of nine integers are and
. The largest possible value of the median of all nine numbers in this list is
$\text{(A)}\ 5\qquad\text{(B)}\6\qquad\text{(C)}\ 7\qquad\text{(D)}\ 8\qquad\text{(E)}\ 9$ (Error compiling LaTeX. Unknown error_msg)
Problem 5
Given that , which of the following is the largest?
Problem 6
If , then
Problem 7
A father takes his twins and a younger child out to dinner on the twins' birthday. The restaurant charges for the father and
for each year of a child's age, where age is defined as the age at the most recent birthday. If the bill is
, which of the following could be the age of the youngest child?
Problem 8
If and
, then
Problem 9
Triangle and square
are in perpendicular planes. Given that
and
, what is
?
Problem 10
How many line segments have both their endpoints located at the vertices of a given cube?
Problem 11
Given a circle of raidus , there are many line segments of length
that are tangent to the circle at their midpoints. Find the area of the region consisting of all such line segments.
Problem 12
A function from the integers to the integers is defined as follows:
Suppose is odd and
. What is the sum of the digits of
?
Problem 13
Sunny runs at a steady rate, and Moonbeam runs times as fast, where
is a number greater than 1. If Moonbeam gives Sunny a head start of
meters, how many meters must Moonbeam run to overtake Sunny?
Problem 14
Let denote the sum of the even digits of
. For example,
. Find
Problem 15
Two opposite sides of a rectangle are each divided into congruent segments, and the endpoints of one segment are joined to the center to form triangle
. The other sides are each divided into
congruent segments, and the endpoints of one of these segments are joined to the center to form triangle
. [See figure for
.] What is the ratio of the area of triangle to the area of triangle ?
Problem 16
A fair standard six-sided dice is tossed three times. Given that the sum of the first two tosses equal the third, what is the probability that at least one "2" is tossed?