Q: 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
A: OK... Stream of consciousness: 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.
The answer is (B).

Q: The average of seven numbers is 4. The average of first three numbers is 2 and the average of last three numbers is 6. What is the middle number?
Options:
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
A: OK... Stream of consciousness: The total of seven numbers = 7X4 = 28
The total of first 3 and last 3 numbers is = 3 X 2+3 X 6 = 24
So, the middle number is (28 - 24 ) = 4
The answer is (B).

Q: Calculate the largest 3 digit number which is exactly divisible by 89?
Options:
(A) 911
(B) 969
(C) 979
(D) 977
(E) 971
A: OK... Stream of consciousness: Largest 4 digit number is 999
After doing 999 ÷ 89 we get remainder 20
Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979
The answer is (C).

Q: What is the are of an equilateral triangle of side 4 cm?
Options:
(A) 64√5
(B) 4√3
(C) 64√4
(D) 64√3
(E) 64√2
A:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
OK... Stream of consciousness: Area of an equilateral triangle = √3/4 S2
If S = 4, Area of triangle = √3/4 * 4 * 4 = 4√3 cm2;
The answer is (B).