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Wendy, Jim, and Pedro are golfing. Collectively, they have

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Wendy, Jim, and Pedro are golfing. Collectively, they have

by BTGmoderatorLU » Fri Oct 19, 2018 2:26 pm

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Source: Manhattan Prep

Wendy, Jim, and Pedro are golfing. Collectively, they have 24 balls. How many golf balls does Jim have?

1. Jim has 1/3 of the number of golf balls that Wendy has.
2. Pedro has 1/2 of the total number of golf balls.

The OA is C.
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Source: — Data Sufficiency |
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by deloitte247 » Sun Oct 21, 2018 2:34 am

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Question= how many golf balls does Jim have
Statement 1= Jim has 1/3 of the number of golf balls that Wendy has.
if Wendy has 3 balls, Jim will have 2 balls and pedro will have 20
if Wendy has 6 balls, Jim will have 2 balls and pedro will have 16
This has more than one solution hence it is NOT SUFFICIENT
Statement 2= Pedro has 1/2 of total golf balls, this means Pedro has 12 balls, the remaining 12 balls can still be either
8 balls to jim, 4 balls to Wendy,
6 balls to jim, 6 balls to Wendy e.t.c.
This statement also has many solutions, hence it is NOT SUFFICIENT.
Combining statement 1 and 2 together Jim has 1/3 0f Wendy's ball and Pedro has 1/2 of total balls.
$$Pedro+Jim+Wendy=24$$
$$Pedro=\frac{1}{2}of\ 24=12$$
$$Let\ Wendy's\ ball=x$$
$$Jim=\frac{1}{3}of\ x$$
$$12+\frac{1}{3}x+x=24$$
$$\frac{1}{3}x+x=24-12$$ $$\frac{\frac{4}{3}x}{\frac{4}{3}}=\frac{12}{\frac{4}{3}}$$
$$x=9$$
Hence, Pedro's ball=12, Wendy's ball=9, and Jim's ball=3
and 12+9+3=24
$$Answer=Option\ C\ $$
both Statements together are SUFFICIENT
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