Probability

If 2 of the 4 expressions x+y, x+5y, x-y & 5x-y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is integer?
A) 1/2
B) 1/3
C) 1/4
D) 1/5
E) 1/6

http://s17.postimage.org/yo824z4jv/2013_03_16_04_40_05.jpg http://s10.postimage.org/5llotrvlh/2013_03_16_04_40_24.jpg Within the STAR you'll see a pentagon(Polygon having 5 sides)--->{in red color, fig. 1} For any polygon, the sum of all the interior angles = 180(n-2), where n is the number of side...

Average

Is the average(arithmetic mean) of 5 different integer atleast 30?
1) Each integer is a multiple of 10
2) The sum of 5 integer is 160

Statement 2 is sufficient(a+b+c+d+e>=30*5-->150)

I need explanation for statement 1.

I will give it a try. It is stated in the report that the sales of dullnic within Fruitland accounted for a small percentage of overall dullnic sales which means the illegally grown drug is also sold in other regions, and that it contributes to much of its sales and option A says that legally grown ...

Inequality

Is x>y>z?
1) x-y = |x-z| + |z-y|
2) x>y

Statement 2 is not sufficient( so B & D can be eliminated).
I need explanation for statement 1

Answer : C Statement 1: 2^x*2^k=4 i.e. x+k=2 here, x=1 k=1 x=2 k=0 x=-2 k=4 etc.. so we cannot ascertain if x>k; therefore not sufficient Statement 2: 9^x*3^k=81 2x+k=4.. not sufficient Combine Statement 1 & 2: we have 2 equations x+k=2 and 2x+k=4.. sufficient as we have 2 variables and 2 equati...

Yes the answer is B.

I think I worked it out the same way:

In statement 2: 9k is divisible by 12, here k has to be 4 or a multiple of 4 in order to be divisible by 12
In statement 1: k has to be 2 or a multiple of 2 in order to be divisible by 16

Thank u!!