Combinatorics + Algebra + Number Theory = The Best :D

Probability Level 4

Let m m be an integer such that 1 ≤ m ≤ 1000 1 \leq m \leq 1000 . Find the probability of selecting at ramdom an integer m m such that the quadratic equation 6 x 2 − 5 m x + m 2 = 0 6x^2 -5mx + m^2=0 has atleast one integer solution.

This question is not my original :D


The answer is 0.667.

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Paul Ryan Longhas
Feb 25, 2015

6 x 2 − 5 m x + m 2 = 0 = > x = m 2 6x^2 -5mx + m^2 =0 => x = \frac{m}{2} or x = m 3 x = \frac{m}{3} .

There are 500 500 multiples of 2, 333 333 multiples of 3, and 166 166 multiples of 6 between 1 and 1000. Therefore, the probability is P r o b a b i l i t y = 500 + 333 − 166 1000 = 0.667 Probability = \frac{500+333-166}{1000} = 0.667

4 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...