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21 Jan 2015, 04:21
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Many different groups apply to march in the annual GLBTGQ, etc. parade. In how many different orders can the groups march, out of the groups chosen to participate in this year’s parade?
1 If the number of groups that will be chosen to march is half of the groups that apply to march, 252 different groups of groups could be chosen to march.
2 If all the groups that applied to march were chosen to march, the groups could march in 3,628,800 orders.
1 If the number of groups that will be chosen to march is half of the groups that apply to march, 252 different groups of groups could be chosen to march.
2 If all the groups that applied to march were chosen to march, the groups could march in 3,628,800 orders.
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21 Jan 2015, 14:45
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Hi chuchu1957,
This DS question is oddly worded (the Official GMAT would be much clearer with the "intent" of the question). I assume that the groups will march in "single file" (one after the next), that there are no other "factors" in how they can be arranged (parade floats, cars, etc. that might appear in a parade) and that it's possible that not all of the groups who APPLY to march in the parade will be allowed to march in the parade.
From a math standpoint, you'll need to understand how permutations and combinations "work" to answer this question.
We're asked for the number of different ORDERS that an unknown number of groups could march in (in a parade). To answer this question, we need to know the number of groups that were CHOSEN to march in the parade.
Fact 1: If HALF the groups who apply are chosen to march, then 252 different sets of groups could be chosen to march.
This Fact hints at the use of the Combination Formula
N!/[K!(N-K)!]
We're told that HALF of the groups would be chosen, so we can relate K to N (K = N/2). Now we have...
N!/[(N/2)!(N - N/2)!) = 252
As "ugly" as this looks, it is just 1 variable in 1 equation, so you CAN solve for N (and by extension, K). This will tell you the number of groups that were chosen.
From a practical standpoint, here's how you can "find" the actual value.
If N = 8 and K = half = 4, then we'd have...
8!/4!4! = (8)(7)(6)(5)/(4)(3)(2)(1) = 70 which is TOO SMALL (it's supposed to be 252)....
If N = 10 and K = half = 5, then we'd have...
10!/5!5! = (10)(9)(8)(7)(6)/(5)(4)(3)(2)(1) = 252 which is an EXACT MATCH. This tells us that 10 groups APPLY and 5 are CHOSEN.
Fact 1 is SUFFICIENT
Fact 2: If ALL the groups who APPLY were CHOSEN, then there would be 3,628,800 orders.
From this Fact, we CAN figure out the number of groups who APPLY:
N! = 3,628,800 which is 1 variable and 1 equation, so we CAN figure out the value of N....
However, we won't know anything about the number that were CHOSEN, so there's no way to answer the question.
Fact 2 is INSUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This DS question is oddly worded (the Official GMAT would be much clearer with the "intent" of the question). I assume that the groups will march in "single file" (one after the next), that there are no other "factors" in how they can be arranged (parade floats, cars, etc. that might appear in a parade) and that it's possible that not all of the groups who APPLY to march in the parade will be allowed to march in the parade.
From a math standpoint, you'll need to understand how permutations and combinations "work" to answer this question.
We're asked for the number of different ORDERS that an unknown number of groups could march in (in a parade). To answer this question, we need to know the number of groups that were CHOSEN to march in the parade.
Fact 1: If HALF the groups who apply are chosen to march, then 252 different sets of groups could be chosen to march.
This Fact hints at the use of the Combination Formula
N!/[K!(N-K)!]
We're told that HALF of the groups would be chosen, so we can relate K to N (K = N/2). Now we have...
N!/[(N/2)!(N - N/2)!) = 252
As "ugly" as this looks, it is just 1 variable in 1 equation, so you CAN solve for N (and by extension, K). This will tell you the number of groups that were chosen.
From a practical standpoint, here's how you can "find" the actual value.
If N = 8 and K = half = 4, then we'd have...
8!/4!4! = (8)(7)(6)(5)/(4)(3)(2)(1) = 70 which is TOO SMALL (it's supposed to be 252)....
If N = 10 and K = half = 5, then we'd have...
10!/5!5! = (10)(9)(8)(7)(6)/(5)(4)(3)(2)(1) = 252 which is an EXACT MATCH. This tells us that 10 groups APPLY and 5 are CHOSEN.
Fact 1 is SUFFICIENT
Fact 2: If ALL the groups who APPLY were CHOSEN, then there would be 3,628,800 orders.
From this Fact, we CAN figure out the number of groups who APPLY:
N! = 3,628,800 which is 1 variable and 1 equation, so we CAN figure out the value of N....
However, we won't know anything about the number that were CHOSEN, so there's no way to answer the question.
Fact 2 is INSUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
21 Jan 2015, 21:46
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EMPOWERgmatRichC
Hi Rich
I agree with your explanation on Fact 1.
But for Fact 2, I don't agree with you and the Official Answer on 2 levels, but please feel free to counter my understanding:
Firstly,
fact 2 states that if ALL the groups who APPLY were CHOSEN, there would be 3,628,800 orders.
Doesn't this statement already sufficiently answer the question?
Q: how many different orders can the chosen group march? A: there would be 3,628,800 orders.
Why do we need to find out the number of CHOSEN (the N value) to answer the question?
Secondly,
since we can theoretically find out the value of N, given that N! = 3,628,800 which is 1 variable and 1 equation,
why do you say that we don't know anything about the number that were CHOSEN?
Isn't value of N = number that were CHOSEN?
Hi Rich
I agree with your explanation on Fact 1.
But for Fact 2, I don't agree with you and the Official Answer on 2 levels, but please feel free to counter my understanding:
Firstly,
fact 2 states that if ALL the groups who APPLY were CHOSEN, there would be 3,628,800 orders.
Doesn't this statement already sufficiently answer the question?
Q: how many different orders can the chosen group march? A: there would be 3,628,800 orders.
Why do we need to find out the number of CHOSEN (the N value) to answer the question?
Secondly,
since we can theoretically find out the value of N, given that N! = 3,628,800 which is 1 variable and 1 equation,
why do you say that we don't know anything about the number that were CHOSEN?
Isn't value of N = number that were CHOSEN?
