question: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a consonant and the last letter has to be a consonant, and each letter can be used only once?
Options:
(A) 21
(B) 42
(C) 1500
(D) 600
(E) 720
answer: Stream of consciousness: Vowel: E O
Consonants: V R M N T
First letter can be filled in 5 Ways ( As the question states that first letter has to be a consonant)
Fifth letter can be filled in 4 Ways ( As the question states that the last letter has to be a consonant)
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 = 5 Ways x 5 Ways x 4 ways x 3 ways x 5 ways = 1500 The answer is (C).
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question: At what rate percent on simple interest will a sum of money double itself in 30 years?
Options:
(A) 3 1/3%
(B) 3 1/8%
(C) 3 6/3%
(D) 9 1/3%
(E) 3 3/3%
answer: Stream of consciousness: P = (P*30*R)/100
R = 3 1/3% The answer is (A).
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question: What is the greatest positive integer x such that 6^x is a factor of 216^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
answer: Stream of consciousness: 216^10 = (6^3)^10 = 6^30 The answer is (E).
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question: Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 610 or over 780. If the individual ranges of the three people's scores in those 4 practice tests were 50, 80 and 90, what is the difference between the maximum and minimum possible ranges of all their scores put together.
Options:
(A) 70
(B) 80
(C) 90
(D) 100
(E) 110
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
Stream of consciousness: According to the information in the question the maximum range would be between 610 and 780(170). The minimum range would be the greatest range for any one individual, which is listed in the problem as 90. So the difference between these would be 170-90 or 80. The answer is (B).
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