[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
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Max@Math Revolution
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A
B
C
D
E
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Keith@ThePrincetonReview
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Plug In the Answers. Begin with choice C.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
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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Max@Math Revolution
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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
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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Scott@TargetTestPrep
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We have the following ratios: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
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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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!
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!
