Quant Probability Problem

GRE Quant Problem Solving
1

There are 4 companies named Q1, Q2, Q3 and Q4. The people in Q1 and Q2 companies are same but the number of people are twice as many in Q3 as Q2. The number of people in Q4 company is greater than Q3 company. But the number of people in Q4 company is less than 3 times of the Q3 company’s people. If randomly chosen from all the four companies, what is the probability of people being picked from Q4 company?

Indicate all the suitable answers.

A) 1/3
B) 5/12
C) 1/2
D) 3/5
E) 11/20

2

1.q1=q2
2.q3=2q2 or 2q1
3.q3<q4<3q3 => 2q1<q4<6q1

assume q4= 2q1 then probability will be 2q1/(q1+q1+2q1+2q1)= 1/3
assume q4=6q1 then probability will be 6q1/(q1+q1+2q1+6q1)=3/5

so now we need to choose a value between these 2 values that is 1/3<p<3/5
so the answer will be b,c,e