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A bag contains ping pong balls, each with a number written

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A bag contains ping pong balls, each with a number written

by AAPL » Thu Jul 04, 2019 6:22 pm

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A bag contains ping pong balls, each with a number written on it. The average of all the numbers is 50. Some of the ping pong balls are removed. What is the average of the numbers on the balls still remaining in the bag?

1. One-third of the ping pong balls are removed from the bag, and the average of the numbers written on those balls is 20.
2. 12 of the ping pong balls are removed from the bag.

OA A
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Source: — Data Sufficiency |

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by Ian Stewart » Fri Jul 05, 2019 3:07 am

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It's a weighted average -- if 1/3 of the pingpong balls average to 20, and all of them average to 50, the other 2/3 will need to average to 65 (since there are twice as many of them as in the 1/3 group, their average will need to be "twice as close" to the overall average). Statement 2 is irrelevant, so the answer is A.
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by deloitte247 » Sat Jul 06, 2019 1:47 pm

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Question => What is the average numbers of the balls still remaining in the bag?

Statement 1: One third of the ping pong balls are removed from the bag, and the average of the numbers written on those balls is 20.
Let the total number of balls in the bag = 30.
Sum of all numbers on the balls is 3N * 50 = 150N
Removing 1/3 rd of 3N => 1/3 * 3N = N
Sum of numbers removed = 20 * N = 20N
$$Average\ of\ remaining\ ball=\frac{\left(150N-20N\right)}{3N-N}=\frac{130N}{2N}=65$$
Statement 1 is SUFFICIENT

Statement 2: 12 of the ping pong balls are removed from the bag.
Information about the total number of balls or numbers on the balls was not provided. Hence, statement 2 is NOT SUFFICIENT.

Conclusively, Statement 1 alone is SUFFICIENT.
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