Question

Let $M$ be the maximum value of the product of two positive integers when their sum is 66. Let the sample space S =\left\\{x \in Z : x(66-x) \geq \frac{5}{9} M\right\\} and the event A =\\{x \in S : x is a multiple of 3\\}. Then $P ( A )$ is equal to

• A. $\frac{15}{44}$
• B. $\frac{1}{3}$
• C. $\frac{7}{22}$
• D. $\frac{1}{5}$

Answer 1

Answer: (B)

$\frac{1}{3}$

Answer 2

M=33×33
x(66−x)≥95​×33×33
11≤x≤55
A:{12,15,18,…54}
P(A)=4515​=31​