An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 8 businessmen, how many possible team submissions are possible?
Options:
(A) 76
(B) 100
(C) 164
(D) 198
(E) 202
Answer and stream of consciousness: (C)
Stream of consciousness: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 8C2 = 112
2) 2 tech1 businessman: 4C2 x 8C1 = 48
3) 3 tech0 businessmen: 4C3 = 4
Total: 112+48+4 = 164

A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
(A) 2287
(B) 27
(C) 299
(D) 287
(E) 150
Answer and stream of consciousness: (E)
Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m

At what rate percent on simple interest will a sum of money double itself in 30 years?
Options:
(A) 3 1/3%
(B) 3 1/9%
(C) 3 9/3%
(D) 3 2/3%
(E) 3 6/3%
Answer and stream of consciousness: (A)
Stream of consciousness: P = (P*30*R)/100
R = 3 1/3%

How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a vowel, and each letter can be used only once?
Options:
(A) 20
(B) 40
(C) 120
(D) 60
(E) 10
Answer and stream of consciousness:
(B)
Stream of consciousness: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)
Fifth letter can be filled in 1 Ways ( As the question states that the last letter has to be a vowel)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 1 ways = 40