q: What is the greatest positive integer x such that 6^x is a factor of 216^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
a: OK... 216^10 = (6^3)^10 = 6^30
The answer is (E).

q: How many numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?
Options:
(A) 496
(B) 486
(C) 1084
(D) 728
(E) 628
a: OK... The number of single digit numbers = 2
The number of 2 digit numbers = 2 3 = 6
The number of 3 digit numbers = 2 3 3 = 18
The number of 4 digit numbers = 2 3 3 3 = 54
The number of 5 digit numbers = 2 3 3 3 3 = 162
The number of 6 digit numbers = 2 3 3 3 3 3 = 486
Therefore, the total numbers = 728
The answer is (D).

q: If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). In a weekly range of temperature recorded at a certain weather station differed by 25 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?
Options:
(A) a) 65/9
(B) b) 13
(C) c) 25
(D) d) 45
(E) e) 81
a:
OK... The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case). Just looking at the answer choices you can pick B which is the only number near half of 25. The other answer choices are too far apart so no need to calculate.
The answer is (B).