Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1996 AHSME Problems"

(→‎Problem 2)
Line 20: Line 20:
  
 
==Problem 3==
 
==Problem 3==
 +
 +
<math> \frac{(3!)!}{3!}= </math>
 +
 +
<math> \text{(A)}\ 1\qquad\text{(B)}\ 2\qquad\text{(C)}\ 6\qquad\text{(D)}\ 40\qquad\text{(E)}\ 120 </math>
  
 
[[1996 AHSME Problems/Problem 3|Solution]]
 
[[1996 AHSME Problems/Problem 3|Solution]]
Line 25: Line 29:
 
==Problem 4==
 
==Problem 4==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
Six numbers from a list of nine integers are <math>7,8,3,5,</math> and <math>9</math>. The largest possible value of the median of all nine numbers in this list is
 +
 
 +
<math> \text{(A)}\ 5\qquad\text{(B)}\6\qquad\text{(C)}\ 7\qquad\text{(D)}\ 8\qquad\text{(E)}\ 9 </math>
 +
 
 +
[[1996 AHSME Problems/Problem 4|Solution]]
  
 
==Problem 5==
 
==Problem 5==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
Given that <math> 0 < a < b < c < d </math>, which of the following is the largest?
 +
 
 +
<math> \text{(A)}\  \frac{a+b}{c+d} \qquad\text{(B)}\ \frac{a+d}{b+c} \qquad\text{(C)}\  \frac{b+c}{a+d} \qquad\text{(D)}\  \frac{b+d}{a+c} \qquad\text{(E)}\ \frac{c+d}{a+b} </math>
 +
 
 +
[[1996 AHSME Problems/Problem 5|Solution]]
  
 
==Problem 6==
 
==Problem 6==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
If <math> f(x) = x^{(x+1)}(x+2)^{(x+3)} </math>, then <math> f(0)+f(-1)+f(-2)+f(-3) = </math>
 +
 
 +
<math> \text{(A)}\ -\frac{8}{9}\qquad\text{(B)}\ 0\qquad\text{(C)}\ \frac{8}{9}\qquad\text{(D)}\ 1\qquad\text{(E)}\ \frac{10}{9} </math>
 +
 
 +
[[1996 AHSME Problems/Problem 6|Solution]]
  
 
==Problem 7==
 
==Problem 7==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 7|Solution]]
  
 
==Problem 8==
 
==Problem 8==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 8|Solution]]
  
 
==Problem 9==
 
==Problem 9==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 9|Solution]]
  
 
==Problem 10==
 
==Problem 10==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 10|Solution]]
  
 
==Problem 11==
 
==Problem 11==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 11|Solution]]
  
 
==Problem 12==
 
==Problem 12==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 12|Solution]]
  
 
==Problem 13==
 
==Problem 13==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 13|Solution]]
  
 
==Problem 14==
 
==Problem 14==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 14|Solution]]
  
 
==Problem 15==
 
==Problem 15==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 15|Solution]]
  
 
==Problem 16==
 
==Problem 16==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 16|Solution]]
  
 
==Problem 17==
 
==Problem 17==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 17|Solution]]
  
 
==Problem 18==
 
==Problem 18==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 18|Solution]]
  
 
==Problem 19==
 
==Problem 19==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 19|Solution]]
  
 
==Problem 20==
 
==Problem 20==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 20|Solution]]
  
 
==Problem 21==
 
==Problem 21==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 21|Solution]]
  
 
==Problem 22==
 
==Problem 22==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 22|Solution]]
  
 
==Problem 23==
 
==Problem 23==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 23|Solution]]
  
 
==Problem 24==
 
==Problem 24==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 24|Solution]]
  
 
==Problem 25==
 
==Problem 25==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 25|Solution]]
  
 
==Problem 26==
 
==Problem 26==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 26|Solution]]
  
 
==Problem 27==
 
==Problem 27==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 27|Solution]]
  
 
==Problem 28==
 
==Problem 28==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 28|Solution]]
  
 
==Problem 29==
 
==Problem 29==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 29|Solution]]
  
 
==Problem 30==
 
==Problem 30==
  
−
[[1996 AHSME Problems/Problem |Solution]]
+
[[1996 AHSME Problems/Problem 30|Solution]]

Revision as of 19:16, 18 August 2011

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)


$\text{(A)}\ 4\qquad\text{(B)}\ 5\qquad\text{(C)}\ 6\qquad\text{(D)}\ 7\qquad\text{(E)}\ 8$


Solution

Problem 2

Each day Walter gets $3$ dollars for doing his chores or $5$ dollars for doing them exceptionally well. After $10$ days of doing his chores daily, Walter has received a total of $36$ dollars. On how many days did Walter do them exceptionally well?

$\text{(A)}\ 3\qquad\text{(B)}\ 4\qquad\text{(C)}\ 5\qquad\text{(D)}\ 6\qquad\text{(E)}\ 7$

Solution

Problem 3

$\frac{(3!)!}{3!}=$

$\text{(A)}\ 1\qquad\text{(B)}\ 2\qquad\text{(C)}\ 6\qquad\text{(D)}\ 40\qquad\text{(E)}\ 120$

Solution

Problem 4

Six numbers from a list of nine integers are $7,8,3,5,$ and $9$. 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)

Solution

Problem 5

Given that $0 < a < b < c < d$, which of the following is the largest?

$\text{(A)}\ \frac{a+b}{c+d} \qquad\text{(B)}\ \frac{a+d}{b+c} \qquad\text{(C)}\ \frac{b+c}{a+d} \qquad\text{(D)}\ \frac{b+d}{a+c} \qquad\text{(E)}\ \frac{c+d}{a+b}$

Solution

Problem 6

If $f(x) = x^{(x+1)}(x+2)^{(x+3)}$, then $f(0)+f(-1)+f(-2)+f(-3) =$

$\text{(A)}\ -\frac{8}{9}\qquad\text{(B)}\ 0\qquad\text{(C)}\ \frac{8}{9}\qquad\text{(D)}\ 1\qquad\text{(E)}\ \frac{10}{9}$

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

Problem 26

Solution

Problem 27

Solution

Problem 28

Solution

Problem 29

Solution

Problem 30

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1996_AHSME_Problems&oldid=41593"