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17 Jun 2018, 06:21
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A
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Difficulty:
55%
(hard)
Question Stats:
64% (01:51) correct
36%
(02:04)
wrong
based on 286
sessions
History
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Not Attempted Yet
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.
(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.
17 Jun 2018, 10:59
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(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 3N = the number of total balls in the bag
The sum of all number on the balls is 3N x 50 = 150N
Then we remove 1/3 of 3N which is N --> The sum of removed number on those balls is N x 20 = 20N
Hence, the average of the remaining balls is (150N - 20N)/(3N - N) = 130N/2N = 65 ---> Sufficient
(2) 12 of the ping pong balls are removed from the bag.
We don't know the total number of balls or any other information about number on those balls. ---> Insufficient
IMO "A"
Let 3N = the number of total balls in the bag
The sum of all number on the balls is 3N x 50 = 150N
Then we remove 1/3 of 3N which is N --> The sum of removed number on those balls is N x 20 = 20N
Hence, the average of the remaining balls is (150N - 20N)/(3N - N) = 130N/2N = 65 ---> Sufficient
(2) 12 of the ping pong balls are removed from the bag.
We don't know the total number of balls or any other information about number on those balls. ---> Insufficient
IMO "A"
17 Jun 2018, 12:19
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Solution
Given:
- • A bag contains ping pong balls, each with a number written on it
• The average of all the numbers is 50
• Some of the balls are removed
To find:
- • The average of the numbers on the balls still remaining in the bag
Analysing Statement 1
- • As per the information given in 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
- o If we assume that originally 3x balls were present in the bag, then x balls are removed
o The total of those removed balls = x * 20 = 20x
o Total sum of all the balls = 50 * 3x = 150x
o Sum of the remaining numbers = 150x – 20x = 130x
o Average of the remaining numbers = \(\frac{130x}{2x}\) = 65
Hence, statement 1 is sufficient to answer
Analysing Statement 2
- • As per the information given in statement 2, 12 balls are removed
- o From this, we don’t know how many balls are left as the total number of balls in the bag is not known
o Also, we have no information about the numbers on those 12 balls which were removed
Hence, statement 2 is not sufficient to answer
Hence, the correct answer is option A.
Answer: A
