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

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by BTGmoderatorDC » Mon Dec 02, 2019 8:40 pm
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

OA E

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by Jay@ManhattanReview » Mon Dec 02, 2019 9:02 pm
BTGmoderatorDC wrote:In a certain game of archery the points in each round for the first, second, third and fourth positions 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

OA E

Source: Manhattan Prep


Given that no other points were given, minimum points Ross earned is 2 and the maximum is 7.

Say Ross was first in a no. of rounds, second in b no. of rounds, thrid in c no. of rounds, and fourth in d no. of rounds. Thus, he participated in (a + b + c + d) rounds.

Thus, we have 21,000 = 7^a*5^b*3^c*2^d

7^1*5^1*3^3*2^3= 7^a*5^b*3^c*2^d

=> a = b = 1 and c = d = 3. Thus, Ross participated in (a + b + c + d = 1 1 + 2 + 2 = 8) rounds.

The correct answer: A

Hope this helps!

-Jay
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