q: How many digits are in the number 50^8 8^3 11?
Options:
(A) 18
(B) 20
(C) 19
(D) 22
(E) 17
a: Stream of consciousness: Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10
50^8 8^3 11 = (5^2*2)^8*2^9*11 = 5^16*2^17*11 = 2*11*10^16 = 22*10^16
Hence we would have 16 trailing 0's and the three digits from 22
Total digits = 2 + 16 = 18 The answer is (A).
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q: The floor of a rectangular room is 15 m long and 12 m wide. The room is surrounded by a verandah of width 2 m on all its sides. The area of the verandah is :
Options:
(A) 124 m2
(B) 120 m2
(C) 108 m2
(D) 58 m2
(E) None of these
a: Stream of consciousness: Area of the outer rectangle = 19 16 = 304 m2
Area of the inner rectangle = 15 12 = 180 m2
Required area = (304 180) = 124 m2 The answer is (A).
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q: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
(A) 17 1/7 days
(B) 27 1/7 days
(C) 23 2/7 days
(D) 16 4/11 days
(E) none of these
a:
Stream of consciousness: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days The answer is (A).
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