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

Revision as of 14:04, 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.

$200-10=190$ $190\times2=380$

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

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

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

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

Revision as of 14:04, 31 July 2011

Problem

Solution

See also