Difference between revisions of "1996 AHSME Problems"
Talkinaway (talk | contribs) (→Problem 11) |
Talkinaway (talk | contribs) (→Problem 12) |
||
Line 92: | Line 92: | ||
==Problem 12== | ==Problem 12== | ||
+ | |||
+ | A function <math>f</math> from the integers to the integers is defined as follows: | ||
+ | |||
+ | <cmath> f(x) =\begin{cases}n+3 &\text{if n is odd}\\ n/2 &\text{if n is even}\end{cases} </cmath> | ||
+ | |||
+ | Suppose <math>k</math> is odd and <math>f(f(f(k))) = 27</math>. What is the sum of the digits of <math>k</math>? | ||
+ | |||
+ | <math> \textbf{(A)}\ 3\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 15 </math> | ||
+ | |||
[[1996 AHSME Problems/Problem 12|Solution]] | [[1996 AHSME Problems/Problem 12|Solution]] |
Revision as of 22:02, 18 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
?