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24 Jan 2025, 01:30
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B
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In a class of 30 students, Emma secured the third rank among the girls, while her brother Ben studying in the same class secured the sixth rank in the whole class. Between the two, who had a better overall rank?
(1) Ben was among the top 25% of the boys merit list in the class in which 60% were boys.
(2) There were three boys among the top five rank holders, and three girls among the top ten rank holders.
(1) Ben was among the top 25% of the boys merit list in the class in which 60% were boys.
(2) There were three boys among the top five rank holders, and three girls among the top ten rank holders.
Updated on: 25 Jan 2025, 05:34
Originally posted by bhargavhhhhhhhh on 24 Jan 2025, 02:01.
Last edited by bhargavhhhhhhhh on 25 Jan 2025, 05:34, edited 1 time in total.
Last edited by bhargavhhhhhhhh on 25 Jan 2025, 05:34, edited 1 time in total.
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Problem:
Determine who had a better overall rank between Emma and Ben.
Statement (1):
- 60% of the 30 students are boys, so there are 18 boys and 12 girls.
- Ben is in the top 25% of the boys’ merit list. 25% of 18 boys = 4.5 → Top 5 boys.
- Ben is the 6th rank overall, which means he is NOT better ranked than Emma (Emma is 3rd among girls and therefore cannot be lower than 6th overall if no other girls outrank Ben).
- Insufficient.
Statement 2 => 3 boys and 2 girls in top 5, means Ben ranks 6th and Emma ranks anywhere b/w 7 - 10th.
As Ben ranks higher than Emma, this statement is sufficient.B
Determine who had a better overall rank between Emma and Ben.
Statement (1):
- 60% of the 30 students are boys, so there are 18 boys and 12 girls.
- Ben is in the top 25% of the boys’ merit list. 25% of 18 boys = 4.5 → Top 5 boys.
- Ben is the 6th rank overall, which means he is NOT better ranked than Emma (Emma is 3rd among girls and therefore cannot be lower than 6th overall if no other girls outrank Ben).
- Insufficient.
Statement 2 => 3 boys and 2 girls in top 5, means Ben ranks 6th and Emma ranks anywhere b/w 7 - 10th.
As Ben ranks higher than Emma, this statement is sufficient.B
24 Jan 2025, 05:56
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30 students
Emma => 3rd rank among girls
Ben => 6th overall
Can we determine relative rank for this two?
Statement 1 => 60% boys = 18 boys and Ben ranks among 25% = 18/4 = top 4 boys
possible ranking sequence can be 3 girls and 3 boys with Emma being 3rd and Ben being 6th, which might lead to Emma having higher rank.
another possibility can be 2 girls and 4 boys with Ben being 6th and Emma being 7th, which leads to Ben having higher rank.
We can't conclude relative ranks, hence insufficient.
Statement 2 => 3 boys and 2 girls in top 5, means Ben ranks 6th and Emma ranks anywhere b/w 7 - 10th.
As Ben ranks higher than Emma, this statement is sufficient.
IMO: B
Emma => 3rd rank among girls
Ben => 6th overall
Can we determine relative rank for this two?
Statement 1 => 60% boys = 18 boys and Ben ranks among 25% = 18/4 = top 4 boys
possible ranking sequence can be 3 girls and 3 boys with Emma being 3rd and Ben being 6th, which might lead to Emma having higher rank.
another possibility can be 2 girls and 4 boys with Ben being 6th and Emma being 7th, which leads to Ben having higher rank.
We can't conclude relative ranks, hence insufficient.
Statement 2 => 3 boys and 2 girls in top 5, means Ben ranks 6th and Emma ranks anywhere b/w 7 - 10th.
As Ben ranks higher than Emma, this statement is sufficient.
IMO: B
