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

(→‎Solution 2 (Brute Force))
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\end{align*}</cmath>
 
\end{align*}</cmath>
  
−
So the answer is <math>\boxed{\text{D}}</math>
+
So the answer is <math>\boxed{\textbf{(D)}\ 200}</math>
 +
~[[shunyipanda]] (Minor edit)
  
 
== Solution 2 (Brute Force) ==
 
== Solution 2 (Brute Force) ==
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Thus the answer is <math>200</math>, or <math>\boxed{\textbf{(D)}\ 200}</math>
 
Thus the answer is <math>200</math>, or <math>\boxed{\textbf{(D)}\ 200}</math>
 +
 +
==Solution 3 (Reasoning)==
 +
As we can see, the numerator is way larger than the denominator so answer choices <math>\boxed{\textbf{(A)}\ .002}</math>, <math>\boxed{\textbf{(B)}\ .2}</math>, and <math>\boxed{\textbf{(C)}\ 20}</math> are eliminated. <math>10^7/10^4</math> is 1000, but in this question the expression, <math>10^7/5 \times 10^4</math>, is smaller than 1000 since the denominator is larger than 10^4. Therefore the answer is <math>\boxed{\textbf{(D)}\ 200}</math>.
 +
~[[shunyipanda]]
  
 
==Video Solution by BoundlessBrain!==
 
==Video Solution by BoundlessBrain!==

Revision as of 20:19, 22 October 2025

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 $\boxed{\textbf{(D)}\ 200}$ ~shunyipanda (Minor edit)

Solution 2 (Brute Force)

$10^7$ is $10000000$

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

Thus the answer is $200$, or $\boxed{\textbf{(D)}\ 200}$

Solution 3 (Reasoning)

As we can see, the numerator is way larger than the denominator so answer choices $\boxed{\textbf{(A)}\ .002}$, $\boxed{\textbf{(B)}\ .2}$, and $\boxed{\textbf{(C)}\ 20}$ are eliminated. $10^7/10^4$ is 1000, but in this question the expression, $10^7/5 \times 10^4$, is smaller than 1000 since the denominator is larger than 10^4. Therefore the answer is $\boxed{\textbf{(D)}\ 200}$. ~shunyipanda

Video Solution by BoundlessBrain!

https://youtu.be/BfFv227egOg

Video Solution

https://youtu.be/KW5HexBjEHU

~savannahsolver

See Also

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


These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. AMC Logo.png

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