houston1980
K, P , V , and W are integers.
\(K^{2} + P^ {2} + V^ {2}+ W^ {2}\) = 100
What is the maximum number of distinct values possible for integer K?
For example if integer H can only take values of 12, 34 and 58, the maximum number of distinct values possible for integer H is 3.
A. 10
B. 11
C. 20
D. 21
E. None of the above
The answer has to be odd, as each value of k will positive and negative + value of 0.Only A, D or E.
Let us write down the squares from 0 to 10.
\(0^2=0\)
\(1^2=1\)
\(2^2=4\)
\(3^2=9\)
\(4^2=16\)
\(5^2=25\)
\(6^2=36\)
\(7^2=49\)
\(8^2=64\)
\(9^2=81\)
\(10^2=100\)
Let us see how many of above with repetition can fit to give us a total of 100.
1) \(100+0+0+0=10^2+0+0+0=100\). So, K can be 0 and |10| => 0, 10, -10
2) \(81+9+1+9=9^2+3^2+3^2+1^2=100\). So, K can be |1|, |3| and |9| => 1, -1, 3, -3, 9, -9
3) \(64+36+0+0=8^2+6^2+0+0=100\). So, K can be |6| and |8| => 6, -6, 8 and -8.
We can mark D as numbers have already reached 13.
4) \(1+49+1+49=1^2+7^2+1^2+7^2=100\). So, K can be |7|. => 7 and -7
5) \(25+25+25+25=5^2+5^2+5^2+5^2=100\). So, K can be |5|, |3| and |9| => 5 and -5.
6) \(64+4+16+16=8^2+2^2+4^2+4^2=100\). So, K can be |8|, |2| and |4| => 2, -2 4 and -4
Total: 21
D