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Selecting a Panel

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 Post subject: Selecting a Panel  Posted: Fri Sep 28, 2012 10:36 pm
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 Question : Selecting a PanelSource : Manhattan GMAT CATA certain panel is to be composed of exactly three women and exactly two men, chosen from x women and y men. How many different panels can be formed with these constraints?(1) If two more women were available for selection, exactly 56 different groups of three women could be selected.(2) x = y + 1My approach was through slot method :___ ___ ___ and ___ ___3 women out of x and 2 men out of yx * (x-1) * (x-2) and y * (y-1) so we got to find what does the above expression evaluate to ?1st statement -> if two more women were available so x is now x+2so women can be chosen in (x+2) * (x+1) * (x) waysand men can be chosen in (y) * (y-1) ways[(x+2) * (x+1) * (x)] * [((y) * (y-1)] = 56 however, this expression won't evaluate to a definite answer hence it is INSUFFICIENT which rules out options A and D2nd statement -> x = y+1Putting y+1 as the value of x in the above expression in blue again wont give me a definite value for the expression hence this statement is INSUFFICIENT which rules out option BCombining both, we get two equations and we have two variables. Although I did not attempt to solve the equations but I think that it will give me the required value for x and y and hence we will be able to evaluate the expression in blue on top and hence combining statement 1 and statement 2 it is SUFFICIENT and hence answer is C.Is my approach incorrect ? Regards

 Post subject: Re: Selecting a Panel  Posted: Mon Oct 01, 2012 5:27 am
 ManhattanGMAT Staff

Posts: 8087
 well, you can do this problem with a lot less work than that.1/no information about the number of men ("y"), so there are an infinite number of possibilities.2/x and y could be, say, 5 and 4. or they could be 1,000,000 and 999,999. or any of infinitely many other possibilities. these are clearly going to give different final answers, so, insufficient.together/from statement 1 you can tell that you're going to get A SPECIFIC # of women.i.e., whenever you add more women, there are more ways to choose 3 of them. so, if you have a specific # of groups possible (here 56), that fixes the number you're choosing from. since this is data sufficiency, you don't have to find that actual number.then, from statement 2, you'll also get a specific # of men.thus you'll have specific numbers all around, so you'll be able to get a specific value for the solution.sufficient.--as far as your slot method:Quote:women can be chosen in (x+2) * (x+1) * (x) waysand men can be chosen in (y) * (y-1) waysthis setup is incorrect. a "panel" is a situation in which order doesn't matter (since there is no particular order, and there are no distinct positions, on a "panel"). so, your product for the women should be divided by 3!, and your product for the men should be divided by 2!. _________________Being well-dressed gives a feeling of inward tranquillity [that] religion is powerless to bestow.C.F. Forbes

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