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Ten friends went to a play arena to play archery. Each of them was

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Ten friends went to a play arena to play archery. Each of them was  [#permalink]

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New post Updated on: 13 Aug 2018, 00:50
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Solve any Median and Range question in a minute- Exercise Question #2

Ten friends went to a play arena to play archery. Each of them was given one arrow each to hit the target. There are five markings on the target: 20, 40, 60, 80 and 100. A person’s score will be zero if he fails to hit the target. At the end of the game, three of them scored 0, one scored 20, two scored 40, one scored 100 and the sum of the scores of remaining three is equal to 240. What was the median score?

Options

    a) 20
    b) 30
    c) 40
    d) 50
    e) 60


To solve question 3: Question 3


To read the article: Solve any Median and Range question in a minute

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Originally posted by EgmatQuantExpert on 11 Jul 2018, 08:01.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:50, edited 3 times in total.
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Re: Ten friends went to a play arena to play archery. Each of them was  [#permalink]

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New post 11 Jul 2018, 08:27
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To find the median score of 10 players

Given the sum of remaining 3 players is 240. The least possible score among these 3 players is a 40. With the given markings, its impossible that one among these 3 has a score of 20. The least score possible has to be a 40(40 + 100 + 100).

Lets try to arrange the scores of 10 players in ascending order by placing the scores on 10 slots

To find the median of 10 slots, we need to know the value of 5th and 6th slot when arranged in ascending order.

3 players scored 0(least possible score)

=> Slot 1 = 0
=> Slot 2 = 0
=> Slot 3 = 0

one player scored 20

=> slot 4 = 20

Since the next lowest possible score is 40 and that is scored by atleast 2 people

=> slot 5 = 40
=> slot 6 = 40

Median = \(\frac{40+40}{2} = 40\)

Hence option C
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Re: Ten friends went to a play arena to play archery. Each of them was  [#permalink]

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New post 11 Jul 2018, 08:44
Median = \(\frac{(5th + 6th )}{2}\)

We know the following order

0,0,0,20,40,40,100
However we need to adjust 3 more scores that total up to 240.

Following are examples of the breakup of 240.

30-105-105 (not possible because only 1 team scored 100 and a score of 105 cannot be included)
40-100-100 (not possible because only 1 team scored 100)


Score 60 and 80 isn't mentioned ann therefore, the breakup of 240 should constitute only 60s and 80s
the only possible combination is
80-80-80

Final order is as follows
0,0,0,20,40,40,80,80,80,100

median = \(\frac{(40+40)}{2} = 40\)
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Re: Ten friends went to a play arena to play archery. Each of them was  [#permalink]

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New post 15 Jul 2018, 05:33

Solution



Given:
• Ten friends are playing archery.
• One can get only one of the six scores: 20, 40, 60, 80 and 100 or 0.
• At the end of the game, three friends scored 0, one friend 20, two friends 40, one friend 100 and the sum of the scores of remaining three is equal to 240

To find:
• The median score of all the three friends.

Approach and Working:

• We can arrange the score of seven friends as: 0, 0, 0 ,20, 40, 40,100

• We still need to find the score of remaining three friends to find the median score.
o Let us assume they scored a, b, and c.
o a + b + c =240
o As maximum score can be 240 only, hence their score can be:
 80,80,80

• In this case, the median will be 40.
 Or 100,100,40

• In this case, the median will be 40.
 Or 100, 80, 60

• In this case, the median will be 40.

In all the cases, the median is 40.
Hence, the correct answer is option C.

Answer: C
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Re: Ten friends went to a play arena to play archery. Each of them was &nbs [#permalink] 15 Jul 2018, 05:33
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