Let the sum of two positive integers be 24 . If the probability, that their product is not less than 3/4 times their greatest positive product, is m/n , where gcd (m, n)=1 , then n-m equals :

Mathematics · Probability

JEE Main 2024 — 8 April, Shift 1 — Question 10

Let the sum of two positive integers be 24 . If the probability, that their product is not less than $\frac{3}{4}$ times their greatest positive product, is $\frac{m}{n}$ , where $\operatorname{gcd}(m, n)=1$ , then $n-m$ equals :

Option A:
9
Option B:
11
Option C:
8
Option D:
10
Correct

Answer: D

Step-by-step solution

$x+y=24, x, y \in N$

$\mathrm{AM}>\mathrm{GM} \Rightarrow \mathrm{xy} \leq 144$

$\mathrm{xy} \geq 108$

Favorable pairs of $(x, y)$ are $(13,11),(12,12),(14,10),(15,9),(16,8),(17,7),(18,6),(6,18),(7,17),(8,16),(9,15),(10,14),(11,13)$

i.e. $13$ cases

Total choices for $\mathrm{x}+\mathrm{y}=24$ is $23$

Probability $=\frac{13}{23}=\frac{m}{n}$

$\mathrm{n}-\mathrm{m}=10$

Answer key and solution verified before publishing.

Practise Probability

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 8 April, Shift 1
Subject: Mathematics
Chapter: Probability
Topic: Problems based on P & C

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively denote the…

Answer: D

Step-by-step solution

Practise Probability

More Probability questions from this paper