In a certain game of archery the points in each round for...

Question

In a certain game of archery the points in each round for the first,second,third and fourth position were 7,5,3,2 . No other points were given. Ross participated in several rounds in the competition and the product of his score was 21000. In How many Rounds Did he participate?
[A] 8
6
[C] 9
[D] 7
[E] Cannot be determined

The OA is E.

I'm confused with this DS question. Please, can any expert assist me with it? Thanks in advanced.

regor60 · Answer

LUANDATO wrote:In a certain game of archery the points in each round for the first,second,third and fourth position were 7,5,3,2 . No other points were given. Ross participated in several rounds in the competition and the product of his score was 21000. In How many Rounds Did he participate?
[A] 8
6
[C] 9
[D] 7
[E] Cannot be determined

The OA is E.

There is an unknown number of rounds and in each round he earned one of the possible scores of 2,3,5 or 7. You also don't know how many of each score was won, but you do know that those will add up to the total number of rounds.

Let W= number of 2 point rounds earned. X = number of 3 point rounds won, Y equal number of 5 point rounds and Z=number of 7 point rounds won.

So W+X+Y+Z = Total number of rounds played. We are looking to determine this number.

Also, per the question, when multiplying the number of 2,3,5,7 point scores together, the total is 21000, so

(2W)(3X)(5Y)(7Z) = 21000

Divided both sides by (2)(3)(5)(7) gives (W)(X)(Y)(Z) = 100

So now the question is, which numbers multiplied together equal 100 and what is their sum ?

Clearly, you could have two 2's and two 5's 2*2*5*5 = 100 and their sum is 14. You could also have 1,1,4,25 whose sum = 31. So because there is more than one choice, the answer can't be determined, E

Notice the question did not ask how many rounds hecould have played. Had that been the question, you would have had to review each of the answer choices to see if they would work.

Brent@GMATPrepNow · Answer

LUANDATO wrote:In a certain game of archery the points in each round for the first,second,third and fourth position were 7,5,3,2 . No other points were given. Ross participated in several rounds in the competition and the product of his score was 21000. In How many Rounds Did he participate?
[A] 8
6
[C] 9
[D] 7
[E] Cannot be determined

Here's how I read it: in each round of play the player receives 7 points, 5 points, 3 points, or 2 points.
21000 = (2)(2)(2)(3)(5)(5)(5)(7)
So, it appears that Ross got three 2's, one 3, three 5's and one 7
Since there's no other way to get a product of 21000 (using 2's, 3's, 5's and 7's only), then Ross must have played 8 rounds.

Am I missing something?

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

regor60 · Answer

Brent@GMATPrepNow wrote:LUANDATO wrote:In a certain game of archery the points in each round for the first,second,third and fourth position were 7,5,3,2 . No other points were given. Ross participated in several rounds in the competition and the product of his score was 21000. In How many Rounds Did he participate? [A] 8 6 [C] 9 [D] 7 [E] Cannot be determined Here's how I read it: in each round of play the player receives 7 points, 5 points, 3 points, or 2 points. 21000 = (2)(2)(2)(3)(5)(5)(5)(7) So, it appears that Ross got three 2's, one 3, three 5's and one 7 Since there's no other way to get a product of 21000 (using 2's, 3's, 5's and 7's only), then Ross must have played 8 rounds. Am I missing something? Cheers, Brent On second thought, I think your way is the correct way to read the question. There was another one like this some time back

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