# Difference between revisions of "1994 AJHSME Problems/Problem 25"

Mrdavid445 (talk | contribs) (Created page with "==Problem== Find the sum of the digits in the answer to <math>\underbrace{9999\cdots 99}_{94\text{ nines}} \times \underbrace{4444\cdots 44}_{94\text{ fours}}</math> where a s...") |
MathsSense (talk | contribs) |
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<math>\text{(A)}\ 846 \qquad \text{(B)}\ 855 \qquad \text{(C)}\ 945 \qquad \text{(D)}\ 954 \qquad \text{(E)}\ 1072</math> | <math>\text{(A)}\ 846 \qquad \text{(B)}\ 855 \qquad \text{(C)}\ 945 \qquad \text{(D)}\ 954 \qquad \text{(E)}\ 1072</math> | ||

+ | |||

+ | ==Solution== | ||

+ | |||

+ | Notice that: | ||

+ | |||

+ | <math>9*4 = 36</math> and <math>3+6 = 9 = 9*1</math> | ||

+ | |||

+ | <math>99*44 = 4536</math> and <math>4+5+3+6 = 18 = 9*2</math> | ||

+ | |||

+ | So the sum of the digits of x 9s times x 4s is simply <math>x*9</math>. | ||

+ | |||

+ | Therefore the answer is <math>94*9 = \boxed{\text{(A)}\ 846}</math> |

## Revision as of 19:25, 14 November 2011

## Problem

Find the sum of the digits in the answer to

where a string of nines is multiplied by a string of fours.

## Solution

Notice that:

and

and

So the sum of the digits of x 9s times x 4s is simply .

Therefore the answer is