Manu and Joby each received a salary increase. Which one received the greater…

Concept: Data sufficiency requires enough information to reach a single, definite answer. Converting a percentage change into an absolute (dollar) amount requires BOTH the percentage AND the original base value — the percentage alone fixes nothing about the absolute change unless the base is also known.

1. Statement (1) alone gives only Manu's percentage increase (8%). Without his original salary, the dollar increase cannot be computed, and nothing at all is known about Joby's raise — so a comparison isn't even possible.

2. Statement (2) alone gives only Joby's percentage increase (5%). Without his original salary, the dollar increase cannot be computed, and nothing is known about Manu's raise either.

3. Combining the statements adds the two percentages together (8% and 5%), but neither original salary is ever revealed. Since dollar increase = percentage × base salary, both bases remain the unknowns needed to compute or compare the actual amounts.

Cross-check: A quick numeric check confirms this: if Manu's base salary were 10,000 and Joby's were 50,000, Manu's rise would be 800 while Joby's would be 2,500 — Joby's dollar increase would be larger despite the smaller percentage. But if Joby's base were only 5,000, his rise would be just 250, making Manu's the larger amount instead. Because the ranking flips depending on the unstated bases, no base-independent conclusion exists.

Result: Since neither statement alone, nor both together, fix the base salaries needed to compute or compare the dollar increases, the data given is not sufficient — statements (1) and (2) TOGETHER are NOT sufficient.