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How many girls are members of both the Diving Team and the Swim Team?
(1) At a joint meeting of the Diving and Swim Teams, no members were absent and 18 girls were present.
(2) The Diving Team has 27 members, one-third of whom are girls, and the Swim Team has 24 members, half of whom are girls.
(1) At a joint meeting of the Diving and Swim Teams, no members were absent and 18 girls were present.
(2) The Diving Team has 27 members, one-third of whom are girls, and the Swim Team has 24 members, half of whom are girls.
31 Jan 2020, 00:31
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How many girls are members of both the Diving Team and the Swim Team?
(1) At a joint meeting of the Diving and Swim Teams, no members were absent and 18 girls were present.
(2) The Diving Team has 27 members, one-third of whom are girls, and the Swim Team has 24 members, half of whom are girls.
(1) At a joint meeting of the Diving and Swim Teams, no members were absent and 18 girls were present.
(2) The Diving Team has 27 members, one-third of whom are girls, and the Swim Team has 24 members, half of whom are girls.
Solution
Look at the diagram:
- • Number of girls in swimming team = \(a\)
• Number of girls in diving team = \(b\)
• Number of girls in both the teams = \(c\)
Statement 1: All the members were present out of which \(18\) girls were present.
- • Total girls considering both teams = \(18\)
- o \(a + b + c = 18\)...(i)
Hence, statement 1 is not sufficient, we can eliminate answer options A and D.
Statement 2: \(b + c =27*\frac{1}{3} = 9\) and \(a + c = 24*\frac{1}{2} =12\)
On adding both the equations, we get
\(a + b + 2c = 12 + 9 = 21\)…(ii)
We can’t find the value of \(c\) with this information.
Hence, statement 2 is not sufficient, we can eliminate options B.
By combining both statements
On subtracting equation (i) from (ii), we get
\(c = 21 – 18 = 3\).
Hence, both the statements combined are sufficient, the correct answer is Option C.
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