# Difference between revisions of "2001 AMC 12 Problems"

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== Problem 2 == | == Problem 2 == | ||

+ | Let <math>P(n)</math> and <math>S(n)</math> denote the product and the sum, respectively, of the digits | ||

+ | of the integer <math>n</math>. For example, <math>P(23) = 6</math> and <math>S(23) = 5</math>. Suppose <math>N</math> is a | ||

+ | two-digit number such that <math>N = P(N)+S(N)</math>. What is the units digit of <math>N</math>? | ||

+ | |||

+ | <math>\text{(A)}\ 2\qquad \text{(B)}\ 3\qquad \text{(C)}\ 6\qquad \text{(D)}\ 8\qquad \text{(E)}\ 9</math> | ||

[[2001 AMC 12 Problems/Problem 2|Solution]] | [[2001 AMC 12 Problems/Problem 2|Solution]] |

## Revision as of 13:56, 16 February 2008

## Contents

- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also

## Problem 1

The sum of two numbers is . Suppose is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?

## Problem 2

Let and denote the product and the sum, respectively, of the digits of the integer . For example, and . Suppose is a two-digit number such that . What is the units digit of ?