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# At the beginning of the summer, swim team A and swim team B each had

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Math Expert
Joined: 02 Sep 2009
Posts: 51055
At the beginning of the summer, swim team A and swim team B each had  [#permalink]

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07 May 2018, 01:57
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:16) correct 35% (00:47) wrong based on 52 sessions

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At the beginning of the summer, swim team A and swim team B each had m members, and no one was a member of both teams. At the end of the summer 6 members left swim team A and 4 members left swim team B. How many members did swim team A have at the beginning of the summer?

(1) The ratio of the total number of members who left the two teams at the end of the year to the total number of members at the beginning of the year is 1/5.
(2) At the end of the summer 21 members remained on swim team B.

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Re: At the beginning of the summer, swim team A and swim team B each had  [#permalink]

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07 May 2018, 02:42

Solution

Given:
• At the beginning of the summer, swim team A and swim team B each had m members, with no common members
• At the end of the summer,
o 6 members left swim team A, members remaining = m – 6
o 4 members left swim team B, members remaining = m – 4
• Total number of members left = 6 + 4 = 10

To find:
• How many members did swim team A have at the beginning of the summer (which is nothing but the value of m)

Analysing Statement 1
• As per the information given in Statement 1, the ratio of the total number of members who left the two teams at the end of the year to the total number of members at the beginning of the year is $$\frac{1}{5}$$
o Or, $$\frac{10}{2m} = \frac{1}{5}$$
Or, m = 25
• Hence, Statement 1 is sufficient to answer

Analysing Statement 2
• As per the information given in Statement 2, at the end of the summer 21 members remained on swim team B
o Or, m – 4 = 21

Or, m = 25
• Hence, Statement 2 is sufficient to answer

Hence, the correct answer is Option D.

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At the beginning of the summer, swim team A and swim team B each had  [#permalink]

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29 Sep 2018, 05:04
Bunuel wrote:
At the beginning of the summer, swim team A and swim team B each had m members, and no one was a member of both teams. At the end of the summer 6 members left swim team A and 4 members left swim team B. How many members did swim team A have at the beginning of the summer?

(1) The ratio of the total number of members who left the two teams at the end of the year to the total number of members at the beginning of the year is 1/5.
(2) At the end of the summer 21 members remained on swim team B.

HiEgmatQuantExpert,

Just a thought, please correct me if it's illogical.
Does swimming happen only in the summer months? If such is not the case then how can we assume that the number who left at the end of year is equal to number who left at the end of summer, there could be more people who left between summer and the end of the year or some could have joined in.We are assuming the number of swimmers at the end of summer equals number of swimmers at the end of the year.
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- Stne

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Joined: 12 Mar 2018
Posts: 73
Re: At the beginning of the summer, swim team A and swim team B each had  [#permalink]

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30 Sep 2018, 15:14
how could we get "year" as "summer"? that was unclear
Re: At the beginning of the summer, swim team A and swim team B each had &nbs [#permalink] 30 Sep 2018, 15:14
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