q: In 2 bags, there are to be put together 5 red and 12 white balls, neither bag being empty. How must the balls be divided so as to give a person who draws 1 ball from either bag-
Options:
(A) 9/18
(B) 9/16
(C) 9/11
(D) 9/12
(E) 9/13
a: Stream of consciousness: (1) Put 1 white in first bag, and all the remaining ball in second bag. Probability = 12×0+12×51612×0+12×516 = 532532
(2) To maximize, we put 1 red in the first bag, and all the remaining in the second. Probability = 12×1+12×43212×1+12×432 = 9/16 The answer is (B).


question: The compound ratio of 2/3, 6/7, 4/3 and 1/8 is given by?
Options:
(A) 2/21
(B) 1/48
(C) 1/98
(D) 1/96
(E) 1/68
answer: Stream of consciousness: 2/3 * 6/7 * 4/3 * 1/8 = 48/504 = 2/21 The answer is (A).


q: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 14 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
Options:
(A)  2,060
(B)  1,320
(C)  545
(D)  364
(E)  220
a: Stream of consciousness: 14*13*12/3*2*1 = 364 The answer is (D).


question: How many 5 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) 21
(B) 42
(C) 120
(D) 600
(E) 720
answer: 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 Fifth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
Fourth letter can be filled in 3 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 3 ways x 1 ways = 120 The answer is (C).


q: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 4 industrial stocks, 5 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
--
Options:
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
a: Stream of consciousness: 4C3 * 5C2 * 3C2 = 4*60*3 = 720. The answer is (E).


q: Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 5 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 7 percent grade, what is x in terms of y and z?
Options:
(A) -1y - 2z
(B) (y +z)  / 4
(C) 2y + 3z
(D) 3y + z
(E) 3y + 4.5z
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
Stream of consciousness: Based on the given information, the following equation could be dervied: 1% * x + 5% * y + 3% * z = 7% * (x+y+z)
Then use algebra to figure out 6%*x = -2%*y - 4%*z. Thus, 3x = -1y - 2z. The answer is (A).