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Difference between revisions of "1997 AJHSME Problems/Problem 2"

(Created page with "The smallest two-digit integer he can subtract is 10. <cmath>200-10=190</cmath> <cmath>190\times2=380</cmath> <math>\boxed{\textbf{(D)}}</math>")
 
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The smallest two-digit integer he can subtract is 10.
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== Problem==
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Ahn chooses a two-digit integer, subtracts it from 200, and doubles the result.  What is the largest number Ahn can get?
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<math>\text{(A)}\ 200 \qquad \text{(B)}\ 202 \qquad \text{(C)}\ 220 \qquad \text{(D)}\ 380 \qquad \text{(E)}\ 398</math>
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==Solution==
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The smallest two-digit integer he can subtract from <math>200</math> is <math>10</math>.  This will give the largest result for that first operation, and doubling it will keep it as the largest number possible.
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<cmath>200-10=190</cmath>
 
<cmath>200-10=190</cmath>
 
<cmath>190\times2=380</cmath>
 
<cmath>190\times2=380</cmath>
  
 
<math>\boxed{\textbf{(D)}}</math>
 
<math>\boxed{\textbf{(D)}}</math>
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== See also ==
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{{AJHSME box|year=1997|num-b=1|num-a=3}}
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* [[AJHSME]]
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* [[AJHSME Problems and Solutions]]
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* [[Mathematics competition resources]]

Revision as of 13:04, 31 July 2011

Problem

Ahn chooses a two-digit integer, subtracts it from 200, and doubles the result. What is the largest number Ahn can get?

$\text{(A)}\ 200 \qquad \text{(B)}\ 202 \qquad \text{(C)}\ 220 \qquad \text{(D)}\ 380 \qquad \text{(E)}\ 398$

Solution

The smallest two-digit integer he can subtract from $200$ is $10$. This will give the largest result for that first operation, and doubling it will keep it as the largest number possible.

\[200-10=190\] \[190\times2=380\]

$\boxed{\textbf{(D)}}$

See also

1997 AJHSME (Problems • Answer Key • Resources)
Preceded by
Problem 1 		Followed by
Problem 3
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
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