Hi guys. This is a tricky one for me.
If two of the four expressions x+y,x+5y, x-y, x-5y are to be selected at random, what is the probability that their product is equal to x^2 - (by)^2 where b is an integer.
a.1/2
b.1/3
c.1/4
d.1/5
e.1/6
Sorry i forgot to add the ans is E
Probability and algebra
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we have the four numbers x+y,x+5y, x-y, x-5y and need to pick 2 number such as the product of the selected numbers is x^2 - (by)^2 i.e.
now we can select the numbers in 4c2 ways (2 numbers out of 4) = 6 ways
now the product should be x^2 - (by)^2 which means they can be factored as
(x-by)*(x+by)
so the pair is
x+y & x-y .... x-5y & x+5y
hence the prob is
2/6 = 1/3
Correct me if wrong ...
regards
sason
now we can select the numbers in 4c2 ways (2 numbers out of 4) = 6 ways
now the product should be x^2 - (by)^2 which means they can be factored as
(x-by)*(x+by)
so the pair is
x+y & x-y .... x-5y & x+5y
hence the prob is
2/6 = 1/3
Correct me if wrong ...
regards
sason
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x^2 - (by)^2 = (x + by)(x - by), which clearly implies that the expressions cannot be x + 5y and x - 5y. So, out of 4 expressions, we are left with 2 expressions.emiflo wrote:Hi guys. This is a tricky one for me.
If two of the four expressions x+y,x+5y, x-y, x-5y are to be selected at random, what is the probability that their product is equal to x^2 - (by)^2 where b is an integer.
a.1/2
b.1/3
c.1/4
d.1/5
e.1/6
Total no. of possible combinations = 4C2 = 6
Therefore, the required probability = 1/6
The correct answer is[spoiler] (E)[/spoiler].
Rahul Lakhani
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https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
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Quant Expert
Gurome, Inc.
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
I didnt get you logic ... can you please explainRahul@gurome wrote:x^2 - (by)^2 = (x + by)(x - by), which clearly implies that the expressions cannot be x + 5y and x - 5y. So, out of 4 expressions, we are left with 2 expressions.emiflo wrote:Hi guys. This is a tricky one for me.
If two of the four expressions x+y,x+5y, x-y, x-5y are to be selected at random, what is the probability that their product is equal to x^2 - (by)^2 where b is an integer.
a.1/2
b.1/3
c.1/4
d.1/5
e.1/6
Total no. of possible combinations = 4C2 = 6
Therefore, the required probability = 1/6
The correct answer is[spoiler] (E)[/spoiler].
1.expressions cannot be x + 5y and x - 5y???
2. shouldnt the answer be 2/6 =1/3 ???
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thanks......but i didn't get our logic can you explain me our logic clearly.........Rahul@gurome wrote:x^2 - (by)^2 = (x + by)(x - by), which clearly implies that the expressions cannot be x + 5y and x - 5y. So, out of 4 expressions, we are left with 2 expressions.emiflo wrote:Hi guys. This is a tricky one for me.
If two of the four expressions x+y,x+5y, x-y, x-5y are to be selected at random, what is the probability that their product is equal to x^2 - (by)^2 where b is an integer.
a.1/2
b.1/3
c.1/4
d.1/5
e.1/6
Total no. of possible combinations = 4C2 = 6
Therefore, the required probability = 1/6
The correct answer is[spoiler] (E)[/spoiler].
GMAT/MBA Expert
- Rahul@gurome
- GMAT Instructor
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- Joined: Sun Apr 11, 2010 9:07 pm
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You are right, I misread the expressions. And the answer to this will be 1/3. Thanks for catching the mistake!sason wrote: I didnt get you logic ... can you please explain
1.expressions cannot be x + 5y and x - 5y???
2. shouldnt the answer be 2/6 =1/3 ???
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)