Difference between revisions of "1999 AHSME Problems/Problem 6"
(Added solution) |
(Formatting) |
||
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
| + | |||
What is the sum of the digits of the decimal form of the product <math> 2^{1999}\cdot 5^{2001}</math>? | What is the sum of the digits of the decimal form of the product <math> 2^{1999}\cdot 5^{2001}</math>? | ||
| Line 6: | Line 8: | ||
<math>2^{1999}\cdot5^{2001}=2^{1999}\cdot5^{1999}\cdot5^{2}=25\cdot10^{1999}</math>, a number with the digits "25" followed by 1999 zeros. The sum of the digits in the decimal form would be <math>2+5=7</math>, thus making the answer <math>\boxed{D}</math>. | <math>2^{1999}\cdot5^{2001}=2^{1999}\cdot5^{1999}\cdot5^{2}=25\cdot10^{1999}</math>, a number with the digits "25" followed by 1999 zeros. The sum of the digits in the decimal form would be <math>2+5=7</math>, thus making the answer <math>\boxed{D}</math>. | ||
| + | |||
| + | == See also == | ||
| + | {{AHSME box|year=1999|before=First question|num-a=2}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Revision as of 20:13, 2 June 2011
Problem
What is the sum of the digits of the decimal form of the product 
?
Solution
, a number with the digits "25" followed by 1999 zeros. The sum of the digits in the decimal form would be 
, thus making the answer 
.
See also
| 1999 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by First question |
Followed by Problem 2 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
