A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
(A) 1/50
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
Answer and stream of consciousness: (A)
Stream of consciousness: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 40/100 = 2/5
Three are independent;probability of rich and fair complexioned girl is:
(1/4) (1/5) (2/5) = 1/50

A motorcyclist goes from Nagpur to Pune, a distance of 500 kms at an average of 100 kmph speed. Another man starts from Nagpur by car 3 hours after the first, and reaches Pune hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
(A) 1:2
(B) 1:7
(C) 3:5
(D) 1:5
(E) 1:1
Answer and stream of consciousness: (C)
Stream of consciousness: T = 500/100 = 10 h
T = 10 - 4 = 6
Time Ratio = 10:6 = 5:3
Speed Ratio = 3:5

In b is a positive integer smaller than 200 and (14b)/60 is an integer, then b has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Answer and stream of consciousness: (B)
Stream of consciousness: 7b/30 tells us that b is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.

Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 540 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
(A) 8/3
(B) 3/8
(C) 8/5
(D) 12/5
(E) 5/3
Answer and stream of consciousness:
(D)
Stream of consciousness: Distance traveled by Eddy = 540 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 540/3 = 180 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 180/75 = 12/5