Difference between revisions of "2006 AMC 10A Problems/Problem 10"
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<math> \mathrm{(A) \ } 3\qquad \mathrm{(B) \ } 6\qquad \mathrm{(C) \ } 9\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 11 </math> | <math> \mathrm{(A) \ } 3\qquad \mathrm{(B) \ } 6\qquad \mathrm{(C) \ } 9\qquad \mathrm{(D) \ } 10\qquad \mathrm{(E) \ } 11 </math> | ||
== Solution == | == Solution == | ||
+ | Since <math>\sqrt{x}</math> cannot be negative, the only integers we get can from our expression are square roots less than 120. The highest is | ||
+ | |||
+ | <math>11^2=121</math> | ||
+ | Thus our set of values is | ||
+ | |||
+ | {<math>11^2, 10^2, 9^2,....2^2, 1^2, 0^2</math>} | ||
+ | |||
+ | And our answer is '''11, (E)''' | ||
== See Also == | == See Also == | ||
*[[2006 AMC 10A Problems]] | *[[2006 AMC 10A Problems]] |
Revision as of 17:01, 3 July 2006
Problem
For how many real values of is
an integer?
Solution
Since cannot be negative, the only integers we get can from our expression are square roots less than 120. The highest is
Thus our set of values is
{}
And our answer is 11, (E)