Let X=\{x|x=2+4k, \text{ where } k=0,1,2,3,...24\}. Let S be a subset of X such that the sum of no two elements of S is 100. What is the <strong>MAXIMUM</strong> possible number of elements in S?

Explanation

Set X has 25 elements: \{2, 6, 10, ..., 98\}. There are 12 disjoint pairs summing to 100 (e.g., 2+98, 6+94) and the standalone element 50. To maximize subset S without forming a pair that sums to 100, select exactly one element from each of the 12 pairs, plus the element 50. Maximum elements = 12 + 1 = 13.

Related questions on Algebra

• If p + q + r = 0, then what is z^{\frac{p^2}{qr}} \times z^{\frac{q^2}{rp}} \times z^{\frac{r^2}{pq}} equal to ?
• What is the value of k for which (k^2 - 5k + 4)x^2 + (k^2 - 3k - 4)x + (k^2 - 4k) = 0 is an identity ?
• If \frac{a^2}{b^2 + c^2} = \frac{b^2}{c^2 + a^2} = \frac{c^2}{a^2 + b^2}, then what is the value of a^4 + b^4 + c^4 equal to ?
• If \frac{1}{x} = \frac{1}{p} + \frac{1}{q}, then what is \frac{pq}{p^2 - q^2}\left(\frac{x + p}{x - p} - \frac{x + q}{x - q}\right) equa...
• If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q) ?