Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space S = x ∈ Z: x(66-x) ≥ (5/9) M and the event A = x ∈ S: x is a multiple of 3 . Then P ( A ) is equal to

Question

Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space S = x ∈ Z: x(66-x) ≥ (5/9) M and the event A = x ∈ S: x is a multiple of 3 . Then P ( A ) is equal to (A) (15/44) (B) (1/3) (C) (7/22) (D) (1/5)

Tardigrade Admin · Accepted Answer

M=33 × 33 x(66-x) ≥ (5/9) × 33 × 33 11 ≤ x ≤ 55 A: 12,15,18, ldots 54 P(A)=(15/45)=(1/3)

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

$\frac{15}{44}$

$\frac{1}{3}$

$\frac{7}{22}$

$\frac{1}{5}$

$M = 33 \times 33$
$x (66 - x) \geq \frac{5}{9} \times 33 \times 33$
$11 \leq x \leq 55$
$A : {12, 15, 18, \dots 54}$
$P (A) = \frac{15}{45} = \frac{1}{3}$

Q. Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space S={x∈Z:x(66−x)≥95​M} and the event A={x∈S:x is a multiple of 3}. Then P(A) is equal to

4415​

31​

227​

51​