1996 AHSME Problems

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)

Solution

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?

Solution

Problem 3

Solution

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)

Solution

Problem 5

Given that , which of the following is the largest?

Solution

Problem 6

If , then

Solution

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?

Solution

Problem 8

If and , then

Solution

Problem 9

Triangle and square are in perpendicular planes. Given that and , what is ?

Solution

Problem 10

How many line segments have both their endpoints located at the vertices of a given cube?

Solution

Problem 11

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Problem 12

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Problem 13

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Problem 14

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Problem 15

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Problem 16

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Problem 17

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Problem 18

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Problem 19

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Problem 20

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Problem 21

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Problem 22

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Problem 23

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Problem 24

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Problem 25

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Problem 26

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Problem 27

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Problem 28

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Problem 29

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Problem 30

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