Difference between revisions of "1985 AJHSME Problems/Problem 3"

Revision as of 21:06, 2 October 2024

Problem

$\frac{10^7}{5\times 10^4}=$

$\text{(A)}\ .002 \qquad \text{(B)}\ .2 \qquad \text{(C)}\ 20 \qquad \text{(D)}\ 200 \qquad \text{(E)}\ 2000$

Solution

We immediately see some canceling. We see powers of ten on the top and on the bottom of the fraction, and we make quick work of this: $\frac{10^7}{5 \times 10^4} = \frac{10^3}{5}$

We know that $10^3 = 10 \times 10 \times 10$ , so

$\begin{align*} \frac{10^3}{5} &= \frac{10\times 10\times 10}{5} \\ &= 2\times 10\times 10 \\ &= 200 \\ \end{align*}$

So the answer is $\boxed{\text{D}}$

Solution 2 (Brute Force)

$10^7$ is $10000000$

$5 \times 10^4$ is $50000$

Thus the answer is $2000$

Video Solution by BoundlessBrain!

https://youtu.be/BfFv227egOg

Video Solution

https://youtu.be/KW5HexBjEHU

~savannahsolver

1985 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 20: / Line 20: @@
 So the answer is <math>\boxed{\text{D}}</math>
-== Solution 2 ==
+== Solution 2 (Brute Force) ==
+<math>10^7</math> is <math>10000000</math>
+<math>5 \times 10^4</math> is <math>50000</math>
+Thus the answer is <math>2000</math>
 ==Video Solution by BoundlessBrain!==

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