Difference between revisions of "2002 AMC 12A Problems"
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== Problem 3 == | == Problem 3 == | ||
| + | According to the standard convention for exponentiation, | ||
| + | <cmath> 2^{2^{2^{2}}} = 2^{(2^{(2^2)})} = 2^{16} = 65536. </cmath> | ||
| + | |||
| + | If the order in which the exponentiations are performed is changed, how many other values are possible? | ||
| + | |||
| + | <math> \mathrm{(A) \ } 0\qquad \mathrm{(B) \ } 1\qquad \mathrm{(C) \ } 2\qquad \mathrm{(D) \ } 3\qquad \mathrm{(E) \ } 4 </math> | ||
[[2002 AMC 12A Problems/Problem 3|Solution]] | [[2002 AMC 12A Problems/Problem 3|Solution]] | ||
Revision as of 22:11, 7 February 2009
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
Compute the sum of all the roots of
Problem 2
Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly?
Problem 3
According to the standard convention for exponentiation,
![\[2^{2^{2^{2}}} = 2^{(2^{(2^2)})} = 2^{16} = 65536.\]](http://latex.artofproblemsolving.com/2/9/d/29dee8eac6c7812722f0013ad002044b30d8f220.png)
If the order in which the exponentiations are performed is changed, how many other values are possible?
Problem 4
Find the degree measure of an angle whose complement is 25% of its supplement.
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?
