q: A family with 1 mother, 1 father, and 4 children sit in a car with 2 front seats and 4 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other three children on either side of him, how many seating arrangements are possible?
Options:
(A) 3
(B) 4
(C) 6
(D) 24
(E) 10
a: Stream of consciousness: Mother has a fixed place and father, so there are 4! ways to arrange the children, hence The answer is (D).
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q: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
Options:
(A) 700
(B) 721
(C) 702
(D) 703
(E) None of the above
a: Stream of consciousness: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60. The answer is (B).
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q: A 600 meter long train crosses a signal post in 20 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
(A) 4 min
(B) 2 min
(C) 8 min
(D) 9 min
(E) 5 min
a:
Stream of consciousness: S = 600/20 = 1530 mps
S = 3600/30 = 120 sec = 2 min The answer is (B).
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