A non-zero integer x is selected randomly from the set of integers x∈Z/−25≤x≤25,x≠0. The probability that x+6≤135x is

n(S)=50E=x satisfied x+6≤135xx2+6x-135≤0 ⇒ (x+15) (x-9)≤0 ⇒ -15≤x≤9n(E)=24P(E)=2450

A non-zero integer x is selected randomly from the set of integers x∈Z/−25≤x≤25,x≠0. The probability that x+6≤135x is

n(S)=50E=x satisfied x+6≤135xx2+6x-135≤0 ⇒ (x+15) (x-9)≤0 ⇒ -15≤x≤9n(E)=24P(E)=2450

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A non-zero integer x is selected randomly from the set of integers $\{x \in Z / - 25 \leq x \leq 25, x \neq 0\}$ . The probability that $x + 6 \leq \frac{135}{x}$ is

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$\frac{3}{5}$

$\frac{12}{25}$

$\frac{14}{25}$

$\frac{2}{5}$

answer is A.

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Detailed Solution

$\begin{array}{rcl} n (S) & = & 50 \\ E & = & \{x satisfied x + 6 \leq \frac{135}{x}\} \\ x^{2} + 6 x - 135 & \leq & 0 \Rightarrow (x + 15) (x - 9) \leq 0 \\ \Rightarrow & - 15 \leq x \leq 9 \\ n (E) & = & 24 \\ P (E) & = & \frac{24}{50} \end{array}$