q: In e is a positive integer smaller than 200 and (14e)/60 is an integer, then e has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
a: Stream of consciousness: 7e/30 tells us that e is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3. The answer is (B).
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q: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is?
Options:
(A) 3377
(B) 2688
(C) 2688
(D) 8436
(E) 1268
a: Stream of consciousness: A = 7500(26/25)^3 = 8436 The answer is (D).
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q: At a meeting of the 6 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 6 Chiefs of Staff be seated around a circular table?
Options:
(A) 120
(B) 480
(C) 4040
(D) 2520
(E) 5040
a:
Stream of consciousness: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (4040), should be the number of ways to arrange all 6 without the seating restriction given. Is this incorrect? The answer is (C).
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