Reasoning: As per the question, let x = 2, y = 6, and z = 12. Plugging these into the answer choices, only A does not yield an integer.
Ans: (A)
Question: If x, y, and z are positive integers such that x is a factor of y and y is a factor of z, which of the following is NOT necessarily an integer?
Options:
(A) (x + y) /z
(B) (y + z) /x
(C) yz/x
(D) (2y + 3z) /x
(E) (xy + z) /y
Rationale: Speed downstream = d/t = 75/(2 1/2) = 30 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (30 - 18)/2 = 6 kmph
The answer: (B)
Question: A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 1 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph
Reasoning: Answer = A
Please refer diagram below
85 - 10 = 75
Ans: (A)
Question: 85 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
Options:
(A) 75
(B) 80
(C) 85
(D) 90
(E) 95
Rationale: (80/100) * 170 â€“ (35/100) * 300
136 - 105 = 31
The answer: (E)
Question: What is the difference between 80% of 170 and 35% of 300.
Options:
(A) 30
(B) 29
(C) 37
(D) 36
(E) 31
Reasoning: His savings in 1 year = 1/4 - (1/8+ 1/12) = 1/24
He can buy a new house in 24 years
Ans: (E)
Question: A man can buy a new house in 4 years with all of his earnings. But he spend the same amount in household expenses in 8 years and for savings in 12 years. How many time needed for buying the house?
Options:
(A) 12
(B) 20
(C) 30
(D) 15
(E) 24
Reasoning: Bass = 2/7 = 10/35
Tuna = 1/5 = 7/35
Trout = 1/7 = 5/35
Catfish = 1 - (10/35 +7/35 + 5/35) = 13/35
Purchased: Tuna = 7/35 - (7/35)(1/7) = 6/35, and
Catfish = 13/35 - (13/35)(1/7) = 12/35
Stocked: doubling the number of bass (2)(10/35) = 20/35
Now: 20 + 6 + 5 + 12 = 43
Trout proportion is now 5/43.
Ans: (C)

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.
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Question: At the A-Street Fish Market a vendor sells fresh caught fish. His store is filled with 2/7 bass, 1/5 tuna, 1/7 trout, and the rest are catfish. If a customer just bought 1/7 of all the tuna and 1/7 of all the catfish, and a fisherman arrived to restock the bass, doubling the number of bass, what proportion of fish now in the store are trout?
Options:
(A) 30/71
(B) 4/7
(C) 5/43
(D) 1/2
(E) 1/5