## Solution
7f/30 tells us that f 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.
## What the question and answer could be
In f is a positive integer smaller than 200 and (14f)/60 is an integer, then f has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
(B)

## Solution
Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by A in 3 minutes = 3/30
Required ratio = 3/30 * 20/11 = 2/11
## What the question and answer could be
Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution P in the liquid in the tank after 3 minutes?
Options:
(A) 3/11
(B) 2/11
(C) 1/11
(D) 4/11
(E) 1/11
(B)

## Solution
Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
## What the question and answer could be
A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 22 sec
(B) 16 sec
(C) 77 sec
(D) 55 sec
(E) 17 sec
(B)

## Solution
Maximum points of intersection between n different circles = n*(n - 1) = 45*44 = 1980
## What the question and answer could be
There are different 45 circles. What is the number of the greatest possible points with which the circles intersect?
Options:
(A) 1950
(B) 2000
(C) 1980
(D) 1580
(E) 2600
(C)