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 "1997 AHSME Problems"

(→‎Problem 2)
(→‎Problem 5)
Line 46: Line 46:
  
 
A rectangle with perimeter <math>176</math> is divided into five congruent rectangles as shown in the diagram.  What is the perimeter of one of the five congruent rectangles?
 
A rectangle with perimeter <math>176</math> is divided into five congruent rectangles as shown in the diagram.  What is the perimeter of one of the five congruent rectangles?
 +
 +
(Note:  Picture needed)
  
 
<math> \mathrm{(A)\ } 35.2 \qquad \mathrm{(B) \ }76 \qquad \mathrm{(C) \  } 80 \qquad \mathrm{(D) \  } 84 \qquad \mathrm{(E) \  }86  </math>
 
<math> \mathrm{(A)\ } 35.2 \qquad \mathrm{(B) \ }76 \qquad \mathrm{(C) \  } 80 \qquad \mathrm{(D) \  } 84 \qquad \mathrm{(E) \  }86  </math>
  
 
[[1997 AHSME Problems/Problem 5|Solution]]
 
[[1997 AHSME Problems/Problem 5|Solution]]

Revision as of 18:39, 7 August 2011

Problem 1

If $\texttt{a}$ and $\texttt{b}$ are digits for which

$\begin{tabular}{r} \texttt{2 a}\ &x \texttt{ b 3} \\ \hline \texttt{6 9}\ & \texttt{9 2 0} \\ \hline \texttt{9 8 9} \end{tabular}$ (Error compiling LaTeX. Unknown error_msg)

then $\texttt{a+b =}$

$\mathrm{(A)\ } 3 \qquad \mathrm{(B) \ }4 \qquad \mathrm{(C) \ } 7 \qquad \mathrm{(D) \ } 9 \qquad \mathrm{(E) \ }12$

Solution

Problem 2

The adjacent sides of the decagon shown meet at right angles. What is its perimeter?

(Note: Picture needed)

$\mathrm{(A)\ } 22 \qquad \mathrm{(B) \ }32 \qquad \mathrm{(C) \ } 34 \qquad \mathrm{(D) \ } 44 \qquad \mathrm{(E) \ }50$

Solution

Problem 3

If $x$, $y$, and $z$ are real numbers such that

$(x-3)^2 + (y-4)^2 + (z-5)^2 = 0$,

then $x + y + z =$

$\mathrm{(A)\ } -12 \qquad \mathrm{(B) \ }0 \qquad \mathrm{(C) \ } 8 \qquad \mathrm{(D) \ } 12 \qquad \mathrm{(E) \ }50$

Solution


Problem 4

If $a$ is $50\%$ larger than $c$, and $b$ is $25\%$ larger than $c$, then $a$ is what percent larger than $b$?

$\mathrm{(A)\ } 20\% \qquad \mathrm{(B) \ }25\% \qquad \mathrm{(C) \ } 50\% \qquad \mathrm{(D) \ } 100\% \qquad \mathrm{(E) \ }200\%$

Solution

Problem 5

A rectangle with perimeter $176$ is divided into five congruent rectangles as shown in the diagram. What is the perimeter of one of the five congruent rectangles?

(Note: Picture needed)

$\mathrm{(A)\ } 35.2 \qquad \mathrm{(B) \ }76 \qquad \mathrm{(C) \ } 80 \qquad \mathrm{(D) \ } 84 \qquad \mathrm{(E) \ }86$

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1997_AHSME_Problems&oldid=41225"