M43-20

Question

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

Bunuel · Answer

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

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

Rebaz · Answer

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!

Bunuel · Answer

The phrase "the number of gymnasts who had worse scores" indeed refers to the number of gymnasts who achieved lower scores in Round 2 compared to Round 1.

SwethaReddyL · Answer

got really confused on how to frame the setup for this question, 
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 - all this comparison to round 1 and round 2, makes me think about taking variables for both r1 and r2 separately - is the wording ambiguous or my understanding is?

Bunuel · Answer

The wording is precise. The comparison to Round 1 and Round 2 is only used to classify each gymnast into one of three groups:

better in Round 2
worse in Round 2
same score in both rounds

komatsu · Answer

I like the solution - it’s helpful.

M43-20

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