Question: How many girls are taller than Shravan in his class? StatementsI.…

Concept

In a descending rank, a person ranked rth from the top has r − 1 people above them.

For a subgroup, subtract the number of subgroup members above the person from the total people above the person to obtain the number above from the complementary subgroup.

Standard ranking questions treat positions as distinct unless ties are stated.

Application

1. From Statement I, Shravan is 17th from the top among all students, so 17 − 1 = 16 students are taller than him.

2. He is 12th from the top among boys, so 12 − 1 = 11 boys are taller than him.

3. Therefore, the number of girls taller than Shravan is 16 − 11 = 5. Statement I determines the requested number independently.

4. From Statement II, 17 boys and 28 students are below Shravan. This gives 28 − 17 = 11 girls below him, but it does not give the total number of girls, so the number of girls above him cannot be found from Statement II alone.

Cross-check

Statement I directly partitions the 16 students above Shravan into 11 boys and 5 girls. Statement II partitions only the students below him, which is not enough to determine how many girls are above him.

Result

I alone is sufficient while II alone is not sufficient.