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A college has a soccer club, a tennis club and a basketball

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by Max@Math Revolution » Fri Jun 08, 2018 1:33 am

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[GMAT math practice question]

A college has a soccer club, a tennis club and a basketball club. Students can enroll in only one of these three clubs. The ratio of the number of soccer club members to the number of tennis club members is 2:3. The ratio of the number of tennis club members to the number of basketball club members is 4:5. A total of 350 students have joined one of these three clubs. How many students are enrolled in the soccer club?

A. 80
B. 90
C. 100
D.120
E. 150
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by Keith@ThePrincetonReview » Sun Jun 10, 2018 11:46 am
Max@Math Revolution wrote:[GMAT math practice question]

A college has a soccer club, a tennis club and a basketball club. Students can enroll in only one of these three clubs. The ratio of the number of soccer club members to the number of tennis club members is 2:3. The ratio of the number of tennis club members to the number of basketball club members is 4:5. A total of 350 students have joined one of these three clubs. How many students are enrolled in the soccer club?

A. 80
B. 90
C. 100
D.120
E. 150
Plug In the Answers. Begin with choice C.

Let S = the number of students in the soccer club, T = the number of students in the tennis club, and B = the number of students in the basketball club.

If S = 100 and the ratio S:T is 2:3, then T = 150 and S + T = 250.
If a total of 350 students joined one of the three clubs, then B = 350 - 250 = 100.
In this case, the ratio T:B is not 4:5, so eliminate choice C.
Since greater values of S entail greater values of T and lesser values of B, eliminate choices D and E as well.

Now test one of the remaining answers. Let's try A.
If S = 80 and the ratio S:T is 2:3, then T = 120 and S + T = 200.
In this case, B = 350 - 200 = 150, and the ratio T:B is 120:150, or 4:5.
The correct answer is choice A.
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by Max@Math Revolution » Sun Jun 10, 2018 5:22 pm
=>
Let S, T and B be numbers of members in the soccer club, the tennis club and the basketball club, respectively.
Since S:T = 2:3 = 8:12 and T:B = 4:5 = 12:15, we have S:T:B = 8:12:15.
Let S = 8k, T = 12k and B = 15k.
Then S + T + B = 8k + 12k + 15k = 35k = 350,
and k = 10.
The number of members of the soccer club is
S = 8k = 80.
Therefore, the answer is A.
Answer: A
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by Scott@TargetTestPrep » Tue Jun 12, 2018 10:15 am
Max@Math Revolution wrote:[GMAT math practice question]

A college has a soccer club, a tennis club and a basketball club. Students can enroll in only one of these three clubs. The ratio of the number of soccer club members to the number of tennis club members is 2:3. The ratio of the number of tennis club members to the number of basketball club members is 4:5. A total of 350 students have joined one of these three clubs. How many students are enrolled in the soccer club?

A. 80
B. 90
C. 100
D.120
E. 150
We have the following ratios:

soccer : tennis = 2 : 3

soccer : tennis = 8 : 12

and

tennis : basketball = 4 : 5

tennis : basketball = 12 : 15

Thus,

soccer : tennis : basketball = 8x : 12x : 15x

So we have:

8x + 12x + 15x = 350

35x = 350

x = 10

So 8(10) = 80 students joined the soccer club.

Answer: A

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by swerve » Tue Jun 12, 2018 11:17 am
Given that the students can enroll in only one of the three clubs. Hence, there is no overlap of members.

Let tennis club members = T
Soccer club members = S
Basketball club members = B

T + S + B = 350 (1)
S/T = 2/3 & T/B = 4/5

Substituting for S in (1) we get S = 80. Option A.

Regards!
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