1990 AJHSME Problems/Problem 21: Difference between revisions
5849206328x (talk | contribs) Created page with '==Problem== A list of <math>8</math> numbers is formed by beginning with two given numbers. Each new number in the list is the product of the two previous numbers. Find the fi…' |
Math-passion (talk | contribs) |
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We just use the definition to find the first number is <math>1/4 \rightarrow \boxed{\text{B}}</math>. | We just use the definition to find the first number is <math>1/4 \rightarrow \boxed{\text{B}}</math>. | ||
==Solution 2== | |||
If we do <math>64/16</math> we get <math>4</math>, then we do <math>16/4</math> giving <math>4</math> again, then <math>4/4</math> is <math>1</math> and <math>4/1</math> is <math>4</math> and finally <math>1/4</math> gives <math>1/4</math> as the answer. Which is <math>\boxed{\text{B}}</math> | |||
==See Also== | ==See Also== | ||
Revision as of 14:47, 22 October 2018
Problem
A list of 
numbers is formed by beginning with two given numbers. Each new number in the list is the product of the two previous numbers. Find the first number if the last three are shown:
![\[\text{\underline{\hspace{3 mm}?\hspace{3 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm} \underline{\hspace{7 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{2 mm}16\hspace{2 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{2 mm}64\hspace{2 mm}}\hspace{1 mm},\hspace{1 mm}\underline{\hspace{1 mm}1024\hspace{1 mm}}}\]](http://latex.artofproblemsolving.com/7/6/2/76215b8f7b52ed31b0c274ef270d019ed2fd160e.png)
Solution
We just use the definition to find the first number is 
.
Solution 2
If we do 
we get 
, then we do 
giving again, then 
is 
and 
is and finally 
gives as the answer. Which is 
See Also
| 1990 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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 | ||
