Here are a couple of recent ones that I am unable to figure out.
If 2 of the 4 expressions, x+y, x+5y, xy, and 5x y are choosen at random, what is the probabilty that their product will be of the form x^2  (by)^2, where b is an integer?
a). 1/2
b). 1/3
c). 1/4
d). 1/5
e). 1/6
The answer is (e)
y< x+z/2 ?
1). yx < zy
2). zy> zx/2
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 jayhawk2001
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Number of ways you can get a pair of expressions from a set of 4 = 4C2mikeclarke44 wrote:Here are a couple of recent ones that I am unable to figure out.
If 2 of the 4 expressions, x+y, x+5y, xy, and 5x y are choosen at random, what is the probabilty that their product will be of the form x^2  (by)^2, where b is an integer?
a). 1/2
b). 1/3
c). 1/4
d). 1/5
e). 1/6
Number of pairs of the form x^2  b.y^2 = 1 [only (x+y)*(xy) ]
So, probability = 1/4C2 = 1/6
Is it (x+z)/2 or x + z/2. Can you please clarify. 1 is sufficientwrote: y< x+z/2 ?
1). yx < zy
2). zy> zx/2
if it is (x+z)/2

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It is (x+z)/2
In the first problem, I did come up with 4C2 = 6, but I thought since there were two combinations it would be 2/6. Close but no cigar!!
In the first problem, I did come up with 4C2 = 6, but I thought since there were two combinations it would be 2/6. Close but no cigar!!
 jayhawk2001
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In that case, is the answer D?mikeclarke44 wrote:It is (x+z)/2
In the first problem, I did come up with 4C2 = 6, but I thought since there were two combinations it would be 2/6. Close but no cigar!!
Rearranging 1, we get 2y < x+z or y < (x+z)/2
Rearranging 2, we get 2z  2y > z  x; 2y < x+z; y < (x+z)/2
Don't worry about not getting the right answer in the first try .
Over time your mind will automatically start to look for patterns
such as this.
So, for the second question, we have both statement (1) and (2) repeating the information given in the question.
For those questions, do we just look at the 2 statements' agreeing with the question as a confirmation of the question? Hence, D?
Or do we have to look at the fact that they're different ways of saying the same thing as in the question? So we're back to square one? Hence, E?
Thoughts???
For those questions, do we just look at the 2 statements' agreeing with the question as a confirmation of the question? Hence, D?
Or do we have to look at the fact that they're different ways of saying the same thing as in the question? So we're back to square one? Hence, E?
Thoughts???

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For the first one...
x^2  (by)^2
I always remember the result listed above can only come from the the form (xy)(x+y)
All the integer values in front of the x's and y's have to be equal so that the middle terms can cancel out.
Looking at your four options that means only the two terms can be multiplied together successfully to achieve the desired result.
Each term has a 1/4 chance of being selected and the remaining necessary term has a 1/3 chance. Hence 1/12. Multiplied by two because either term could be selected first or second and there you go...
Its not pretty, but its a different way of looking at it...
x^2  (by)^2
I always remember the result listed above can only come from the the form (xy)(x+y)
All the integer values in front of the x's and y's have to be equal so that the middle terms can cancel out.
Looking at your four options that means only the two terms can be multiplied together successfully to achieve the desired result.
Each term has a 1/4 chance of being selected and the remaining necessary term has a 1/3 chance. Hence 1/12. Multiplied by two because either term could be selected first or second and there you go...
Its not pretty, but its a different way of looking at it...

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can someone explain 4C2. I thought the answer would be 4*3.
4 possiblities from choice 1, 3 possibilities from choice 3.
4 possiblities from choice 1, 3 possibilities from choice 3.