If there are 4 seats and two students, in how many ways can they be seated?
Options:
(A) 12
(B) 6
(C) 8
(D) 16
(E) 10
--
No. of ways of choosing 2 chairs out of 4 chairs on which two students will sit = 4C2 = 6
No. of ways of 2 people sitting on selected chairs = 2!
Total ways of making 2 people sit on 2 of 4 chairs = 4C2*2! = 6*2 = 12 So the answer is: (A).
-----
What is the maximum number of pieces of birthday cake of size 3" by 3" that can be cut from a cake 21" by 21"?
Options:
(A) 5
(B) 7
(C) 49
(D) 20
(E) 25
--
The prompt is essentially asking for the maximum number of 3x3 squares that can be cut from a larger 21 by 21 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 7 'pieces' each, we have (7)(7) = 49 total smaller squares (at maximum). So the answer is: (C).
-----
The speed of a boat in still water is 80kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
--
Speed downstream = 80 + 20 = 100 kmph
Speed upstream = 80 - 20 = 60 kmph So the answer is: (D).
-----