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

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A college has a soccer club, a tennis club and a basketball club. St [#permalink]

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New post 08 Jun 2018, 02:44
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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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A college has a soccer club, a tennis club and a basketball club. St [#permalink]

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New post 08 Jun 2018, 02:52
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MathRevolution 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


The ratio of members in the Soccer and Tennis clubs is 2:3.
For every 2x Soccer club members, we will have 3x Tennis club members.

The ratio of members in the Tennis and Basketball clubs is 4:5.
For every 4y Tennis Club members, we have 5y basketball members.

To make the ratios comparable, x = 4 and y = 3.
Now, Soccer : Tennis = 8:12 and Tennis : Basketball = 12:15. Overall ratio Soccer:Tennis:Basketball - 8:12:15

Therefore, the number of students who are enrolled in the soccer clue is \(\frac{8}{8+12+15} * 350 = \frac{8}{35} * 350 = 80\)(Option A)
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Re: A college has a soccer club, a tennis club and a basketball club. St [#permalink]

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New post 08 Jun 2018, 03:25
MathRevolution 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


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..........eq.(i)

S/T = 2/3 & T/B = 4/5

Substituting for S in eq.(i)

We get S = 80

Answer A.

Thanks,
GyM
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Re: A college has a soccer club, a tennis club and a basketball club. St [#permalink]

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New post 10 Jun 2018, 18:36
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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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Re: A college has a soccer club, a tennis club and a basketball club. St [#permalink]

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New post 12 Jun 2018, 11:14
MathRevolution 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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Re: A college has a soccer club, a tennis club and a basketball club. St   [#permalink] 12 Jun 2018, 11:14
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