q: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is
Options:
(A) 10/17
(B) 10/19
(C) 46/105
(D) 11/15
(E) Cannot be determined
a: Stream of consciousness: There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined. The answer is (E).
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q: How many factors does 49^2 have?
Options:
(A) 2
(B) 8
(C) 24
(D) 25
(E) 36
a: Stream of consciousness: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 6*6 = 36 The answer is (E).
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q: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible?
Options:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
a:
Stream of consciousness: Mother has a fixed place and father, so there are 2! ways to arrange the children, hence The answer is (A).
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