Problem Solving

Source of problems - www.mba.com - Practice Test 2
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Question 1.

If two of the four expressions x+y, x+5y, x-y, 5x-y are chosen at random, what is the probablity that their product will be of the form x^2 - (by^2) were b is an integer
a) 1/2
b) 1/3
c) 1/4
d) 1/5
e) 1/6

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Question 2.

Which of the following lists the number of points at which a circle can intersect a triangle?
a) 2 and 6 only
b) 2,4 and 6 only
c) 1,2,3 and 6 only
d) 1,2,3,4 and 6 only
e) 1,2,3,4,5 and 6






Answers
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1. Answer is E. My probablity is not too good, but this doesn't seem hard. I got C) - Any probablity tips for easier questions ?

2. Answer is E. Is there a technique or purpose behind this problem ? Or just brute force of drawing various diagrams ? I got it right, just thought it was a rather silly problem.

For question 1 --

Number of ways you can get a product = 4C2 = 6
Number of products that can be of form x^2 - bY^2 = 1
[only (x+y)(x-y) satisfies the above condition ]

So, probability = 1/6

For question 2 --

Not sure if there's an associated diagram with the question. If no diagram,
then a triangle can intersect a circle at max of 6 points. Each side of the
triangle can cut the circle at 2 points for a total of 6 points.

If two of the four expressions x+y, x+5y, x-y, 5x-y are chosen at random, what is the probablity that their product will be of the form x^2 - (by^2) were b is an integer
a) 1/2
b) 1/3
c) 1/4
d) 1/5
e) 1/6

The total possible number of outcomes are 4C2 (4 expressions taken 2 at a time)

4C2 = 4!/2!*2! = 6

Total number of times we can get a product of the order x^2 - (by^2) is only 1 i.e. (x+y) (x-y)

Hence the probability is 1/6

2) Where is the diagram???

hey is it x^2 -(by)^2? cause if it is not then does not (x+5y)(x-y) give me
x^2-(5y^2)?? please explain...

never mind stupidity just got the better of me carry on ! thanks!!!!!