Ques: John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true?
Options:
(A) 201
(B) 301
(C) 401
(D) 101
(E) 501
Ans: (B)
CoT: The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1. For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.

Ques: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 170 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 3 sec
(B) 8 sec
(C) 9 sec
(D) 5 sec
(E) 7 sec
Ans: (B)
CoT: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 170 + 100 = 270 m
T = 270 * 3/100 = 8 sec

Ques: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
(A) 5
(B) 4
(C) 3
(D) 6
(E) 8
Ans: (C)
CoT: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.

Ques: How much 80% of 40 is greater than 10% of 15?
Options:
(A) 18
(B) 99
(C) 19
(D) 18
(E) 17
Ans: (E)
CoT: (80/100) * 40 (10/100) * 15
32 - 15 = 17