Difference between revisions of "2002 AMC 12P Problems/Problem 7"

Revision as of 23:45, 29 December 2023

Problem

How many three-digit numbers have at least one $2$ and at least one $3$ ?

$\text{(A) }52 \qquad \text{(B) }54 \qquad \text{(C) }56 \qquad \text{(D) }58 \qquad \text{(E) }60$

Solution

If $\log_{b} 729 = n$ , then $b^n = 729$ . Since $729 = 3^6$ , $b$ must be $3$ to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of $b \Longrightarrow \boxed{\mathrm{E}}$ .

2002 AMC 12P (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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All AMC 12 Problems and Solutions

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

@@ Line 1: / Line 1: @@
 == Problem ==
-How many three-digit numbers have at least one <math>2</math> and at least one <math>3?</math>
+How many three-digit numbers have at least one <math>2</math> and at least one <math>3</math>?
 <math>

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Difference between revisions of "2002 AMC 12P Problems/Problem 7"

Revision as of 23:45, 29 December 2023

Problem

Solution

See also