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Difference between revisions of "1980 AHSME Problems/Problem 9"
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<math>\text{(A)} \ \sqrt 3 \qquad \text{(B)} \ 2\sqrt{5} \qquad \text{(C)} \ \frac 32 \qquad \text{(D)} \ 3 \qquad \text{(E)} \ \text{not uniquely determined}</math>
 
<math>\text{(A)} \ \sqrt 3 \qquad \text{(B)} \ 2\sqrt{5} \qquad \text{(C)} \ \frac 32 \qquad \text{(D)} \ 3 \qquad \text{(E)} \ \text{not uniquely determined}</math>
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== Solution ==
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Let us think about this. We only know that he ends up <math>\sqrt{3}</math> away from the origin. However, think about the locus of points <math>\sqrt{3}</math> away from the origin, a circle. However, his path could end on any part of the circle below the <math>x-</math>axis, so therefore, the answer is
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<math>\fbox{E: not uniquely determined}.</math>
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(Note: Another way to do this is using law of cosines, which yields two solutions for x.)
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== See also ==
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{{AHSME box|year=1980|num-b=8|num-a=10}} 
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[[Category: Introductory Algebra Problems]]
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 15:00, 20 March 2018

Problem

A man walks $x$ miles due west, turns $150^\circ$ to his left and walks 3 miles in the new direction. If he finishes a a point $\sqrt{3}$ from his starting point, then $x$ is

$\text{(A)} \ \sqrt 3 \qquad \text{(B)} \ 2\sqrt{5} \qquad \text{(C)} \ \frac 32 \qquad \text{(D)} \ 3 \qquad \text{(E)} \ \text{not uniquely determined}$

Solution

Let us think about this. We only know that he ends up $\sqrt{3}$ away from the origin. However, think about the locus of points $\sqrt{3}$ away from the origin, a circle. However, his path could end on any part of the circle below the $x-$axis, so therefore, the answer is $\fbox{E: not uniquely determined}.$

(Note: Another way to do this is using law of cosines, which yields two solutions for x.)

See also

1980 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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