A and B can do a work in 6 days, B and C in 2 days and C and A in 8 days. In how many days will the work be completed, if all three of them work together?
Options:
(A) 12/24
(B) 48/63
(C) 45/56
(D) 48/19
(E) 28/12
--
One day work of A and B = 1/6
One day work of B and C = 1/2
One day work of C and A = 1/8
2(A + B + C) = 1/6 + 1/2 + 1/8
2(A + B + C) = 19/24
(A + B + C) = 19/48
Number of days required = 48/19 days. So the answer is: (D).
-----
The difference between the local value and the face value of 7 in the numeral 32675149 is
Options:
(A) 69950
(B) 69993
(C) 69997
(D) 70000
(E) 01000
--
(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993 So the answer is: (B).
-----
In f is a positive integer smaller than 200 and (14f)/60 is an integer, then f has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
--
7f/30 tells us that f 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. So the answer is: (B).
-----