In a class of 30 students, Emma secured the third rank among the girls

Hi Nailin16,

This question does not test us too much on Math but tests us more on reasoning. The best thing to do when we have a logical reasoning question is to take stock of all the data given and try to put some structure around the data by tabulating it.

The information we need to hold onto here is that Ben secures the sixth rank in the whole class and Emma secured the third rank among the girls.

Statement 1 : Ben was among the top 25% of the boys merit list in the class in which 60% were boys.

Since 60% of the 30 students were boys, the number of boys is 18 and the number of girls is 12. Ben also needs to rank in the top 4 among the boys (25% of 18 = 4.5). Now since Ben's rank with respect to the entire class is fixed we can represent the ranks as follows



So we can have Emma to have a higher overall rank or Ben to have a higher overall rank. Insufficient.

Statement 2 : There were three boys among the top five rank holders, and three girls among the top ten rank holders.

Again Ben's rank with respect to the entire class is fixed. So tabulating the data give in the second statement we get.



We need to keep in mind that Emma must always ranks 3rd among the girls.

In the first scenario let three boys achieve the top 3 ranks and 2 girls occupy the next two ranks. Since Ben's position is fixed at rank 6, Emma will have to rank below Ben.

In the second scenario let 2 girls achieve the top 2 ranks (we cannot have all 3 girls to achieve the top 3 ranks since we need 3 boys in the top 5). Since the next three ranks (ranks 3,4 and 5) are achieved by boys and Ben's rank is fixed at 6, Emma again has to rank below Ben. Sufficient.

OA : B

CrackVerbal Academics Team