A bag contains pieces worth 3,5 and 11 points,respectievly. During a turn, a player selects upto 10 pieces at random

BTGmoderatorDC wrote: ↑

Thu Jul 23, 2020 6:13 pm

A bag contains pieces worth 3, 5, and 11 points, respectively. During a turn, a player selects up to 10 pieces at random from the bag. The player's score for the turn is found by taking the product of the point values of each selected piece. If Jake's score for a turn is 12375, how many total pieces did he select?

A)2
B)3
C)4
D)5
E)6

OA E

Source: Princeton Review

Say Jake selected x no. of pieces of 3 points; y no. of pieces of 5 points; z no. of pieces of 11 points.

Thus, the total no. of pieces selected = x + y + z

So, we have 3^x*5^y*11^z = 12,375

3^x*5^y*11^z = 3^2*5^3*11^1

Thus, the total no. of pieces selected = x + y + z = 2 + 3 + 1 = 6

Correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Thu Jul 23, 2020 6:13 pm

A bag contains pieces worth 3,5 and 11 points,respectievly. During a turn, a player selects upto 10 pieces at random from the bag.The player's score for the turn is found by taking the product of the point values of each selected piece.If Jake's score for aturn is 12375,how many total pieces did he select?

A)2
B)3
C)4
D)5
E)6


OA E

Solution:

We are given that a bag contains pieces worth 3, 5, and 11 points, respectively, and that Jake scores 12375. We need to determine how many pieces he selected. Let’s break 12,375 into primes.

12,375 = 25 x 495 = 25 x 5 x 99 = 5^2 x 5^1 x 3^2 x 11^1 = 3^2 x 5^3 x 11^1

Thus, Jake pulled 2 threes, 3 fives, and 1 eleven for a total of 6 pieces.

Answer: E