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29 Jul 2024, 05:12
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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
29 Jul 2024, 05:12
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Official Solution:
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:
\(x + 1.25x + 2.5x = 38\)
\(4.75x = 38\)
\(x = 8\)
Therefore, the number of gymnasts who achieved better scores would be \(1.25x = 10\).
Answer: C
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:
\(x + 1.25x + 2.5x = 38\)
\(4.75x = 38\)
\(x = 8\)
Therefore, the number of gymnasts who achieved better scores would be \(1.25x = 10\).
Answer: C
05 Dec 2024, 04:51
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Bunuel
My problem with this question is with the last part: the number of gymnasts who had worse scores
Does this mean the The number of gymnasts who achieved lower scores in Round 2 compared to Round 1?
Thanks in Advance!
Quote:
My problem with this question is with the last part: the number of gymnasts who had worse scores
Does this mean the The number of gymnasts who achieved lower scores in Round 2 compared to Round 1?
Thanks in Advance!
