Geetanjali got the 15th rank among the girls in the class. How many girls are…

CONCEPT: In a Data Sufficiency question, a statement is sufficient only if it fixes ONE definite value for the quantity asked. Test each statement alone first; only combine them if neither one alone gives a unique value.

1. Statement I alone: Shilpa ranked last among the girls. This only tells us that a bottom rank exists; it never states what number that last rank is, so the class size cannot be found from this fact alone.

2. Statement II alone: Shilpa ranked next to Geetanjali, so Shilpa's rank is either 14th or 16th. Two possible values remain, and neither is tied to the size of the class, so this fact alone is not enough either.

3. Both together: Shilpa is the last-ranked girl, so Shilpa's rank number equals the total count of girls and must be at least as large as Geetanjali's rank (15th) - the last position cannot outrank anyone. Of the two candidates from Statement II, 14 is smaller than 15 and is therefore impossible for the last rank, leaving 16 as the only consistent value.

CROSS-CHECK: With 16 girls, Geetanjali is 15th and Shilpa is 16th - Shilpa sits immediately next to Geetanjali (matches Statement II) and Shilpa's 16th rank is indeed the last position among 16 girls (matches Statement I). Both facts are satisfied by exactly one class size.

So both statements put together are sufficient, while neither statement alone is.