Reasoning: (6n^2 + 6n) = 6n(n + 1), which is divisible by both 6 and 12, since n(n+1) is always even.
Ans: (B)
Question: If n is a natural number, then (6n^2 + 6n) is always divisible by
Options:
(A) 6 only
(B) 6 and 12 both
(C) 12 only
(D) 18 only
(E) 12 and 18 both
Rationale: It's a simple geometry problem. Look at the diagram below:
The answer: (A)
Question: Efrida and Frazer who live 10 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is four miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
Options:
(A) 6
(B) 7
(C) 8
(D) 10
(E) 11
Reasoning: In the beginning it is 99 pounds water and 1 pound other stuff. At the end the 1 pound other stuff is 2 percent so the total weight is 50 pounds. 50 pounds - 1 pound other stuff = 49 pounds water. So 99 pounds - 49 pounds = 50 pounds water lost.
Ans: (D)
Question: There is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.
How much water evaporated?
Options:
(A) 20
(B) 30
(C) 40
(D) 50
(E) 10
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
The answer: (E)
Question: Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 1234
(B) 2343
(C) 4546
(D) 3435
(E) 5184
Reasoning: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph
Ans: (D)
Question: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) 22 kmph
(B) 40 kmph
(C) 78 kmph
(D) 50 kmph
(E) 23 kmph
Reasoning: Let's assume that a is an even prime integer and b is an odd prime integer, their subtraction results in an odd integer and an odd integer multiplied by an even integer yields an even integer.
Ans: (C)
Question: If a and b are unique prime integers, which of the following must be even?
Options:
(A) ab
(B) a2b
(C) 2a2b
(D) 2ab
(E) ab^2