2011 CEMC Gauss (Grade 7) Problems/Problem 11

Problem

In the diagram, the value of $x$ is

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$\textbf{(A)}\ 15 \qquad\textbf{(B)}\ 20 \qquad\textbf{(C)}\ 22 \qquad\textbf{(D)}\ 18 \qquad\textbf{(E)}\ 36$

Solution 1

From the diagram, we can see that $2x$ and $3x$ sum up to $90$ due to the right angle. Thus, we have:

$2x + 3x = 90$

$5x = 90$

$x = \frac{90}{5} = \boxed {\textbf {(D) } 18}$

~anabel.disher

Solution 2 (answer choices)

Since the expression is $5x$ , we can plug-in values for $x$ until we get $90$ degrees.

$20 \times 5 = 100$ . This is more than $90$ , so $20$ and everything above it cannot be correct for $x$ . This eliminates answer choices B, C, and E.

$15 \times 5 = 75$ . This is less than $90$ , eliminating answer choice A.

Because all of the other answer choices have been eliminated, the answer is $\boxed {\textbf {(D) } 18}$

2011 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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2011 CEMC Gauss (Grade 7) Problems/Problem 11

Problem

Solution 1

Solution 2 (answer choices)