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19 Jul 2024, 07:00
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C
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35%
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79% (02:26) correct
21%
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At an Olympic gymnastics competition, 38 gymnasts competed in both Round 1 and Round 2. The number of gymnasts who achieved better scores in Round 2 compared to Round 1 was 25% greater than the number of gymnasts who had worse scores. Additionally, the number of gymnasts who received the same score in both rounds was twice the number of gymnasts who achieved better scores in Round 2 compared to Round 1. How many gymnasts had better scores in Round 2 compared to Round 1?
A. 6
B. 8
C. 10
D. 12
E. 20
A. 6
B. 8
C. 10
D. 12
E. 20
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19 Jul 2024, 08:15
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At an Olympic gymnastics competition, 38 gymnasts competed in both Round 1 and Round 2. The number of gymnasts who achieved better scores in Round 2 compared to Round 1 was 25% greater than the number of gymnasts who had worse scores. Additionally, the number of gymnasts who received the same score in both rounds was twice the number of gymnasts who achieved better scores in Round 2 compared to Round 1. How many gymnasts had better scores in Round 2 compared to Round 1?
A. 6
B. 8
C. 10
D. 12
E. 20
Assuming the number of gymnasts who achieved worse scores was x, the number of gymnasts who achieved better scores would be 25% greater than that, so 1.25x. The number of gymnasts who received the same score would be twice the number receiving better scores, so 2 * 1.25x = 2.5x.
Given that the total number of gymnasts was 38, we get:
Therefore, the number of gymnasts who achieved better scores would be 1.25x = 10.
Answer: C.
GMAT Club Official Explanation:
At an Olympic gymnastics competition, 38 gymnasts competed in both Round 1 and Round 2. The number of gymnasts who achieved better scores in Round 2 compared to Round 1 was 25% greater than the number of gymnasts who had worse scores. Additionally, the number of gymnasts who received the same score in both rounds was twice the number of gymnasts who achieved better scores in Round 2 compared to Round 1. How many gymnasts had better scores in Round 2 compared to Round 1?
A. 6
B. 8
C. 10
D. 12
E. 20
Assuming the number of gymnasts who achieved worse scores was x, the number of gymnasts who achieved better scores would be 25% greater than that, so 1.25x. The number of gymnasts who received the same score would be twice the number receiving better scores, so 2 * 1.25x = 2.5x.
Given that the total number of gymnasts was 38, we get:
x + 1.25x + 2.5x = 38
4.75x = 38
x = 8
4.75x = 38
x = 8
Therefore, the number of gymnasts who achieved better scores would be 1.25x = 10.
Answer: C.
General Discussion
19 Jul 2024, 07:10
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Given: At an Olympic gymnastics competition, 38 gymnasts competed in both Round 1 and Round 2. The number of gymnasts who achieved better scores in Round 2 compared to Round 1 was 25% greater than the number of gymnasts who had worse scores. Additionally, the number of gymnasts who received the same score in both rounds was twice the number of gymnasts who achieved better scores in Round 2 compared to Round 1.
Asked: How many gymnasts had better scores in Round 2 compared to Round 1?
Total gymnasts = 38
Let the number of gymnasts who had better scores in Round 2 compared to Round 1 be x.
The number of gymnasts who had worse scores in Round 2 compared to Round 1= x/1.25 = 4x/5
The number of gymnasts who had same scores in both rounds = 2x
Total number of gymnasts = x + 4x/5 + 2x = 38
19x/5 = 38
x = 38*5/19 = 10
The number of gymnasts who had better scores in Round 2 compared to Round 1 = x = 10\
IMO C
Asked: How many gymnasts had better scores in Round 2 compared to Round 1?
Total gymnasts = 38
Let the number of gymnasts who had better scores in Round 2 compared to Round 1 be x.
The number of gymnasts who had worse scores in Round 2 compared to Round 1= x/1.25 = 4x/5
The number of gymnasts who had same scores in both rounds = 2x
Total number of gymnasts = x + 4x/5 + 2x = 38
19x/5 = 38
x = 38*5/19 = 10
The number of gymnasts who had better scores in Round 2 compared to Round 1 = x = 10\
IMO C
