question:P and Q invested in a shop. The profits were divided in the ratio of 4 : 6 respectively. If P invested Rs. 55,000, the amount invested by Q is:
Options:
(A) 48000
(B) 40000
(C) 35000
(D) 60000
(E) None
answer:(E)
Stream of consciousness:Suppose Q invested Rs. y. Then, 50000/y = 4/6 or y = [50000 x 6/ 4] = 75000.


question:If 10 crates have 97 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 30
(B) 10
(C) 15
(D) 20
(E) 0
answer:(A)
Stream of consciousness:Each crate requires 3 apples and totally there are 10 crates so required apples = 10 * 3 = 30


question:Fifteen coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
(A) 2^9
(B) 2^14
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
answer:

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
(B)
Stream of consciousness:Fix the third coin as H. The remaining 14 coins have 2^14 outcomes.