Notice that t^2 + 5t + 6 = (t + 2)(t + 3).
1. what 1 tells us that t = 7k + 6. Replace this in the initial (t + 2)(t + 3) = (7k + 6 + 2)(7k + 6 + 3) = (7k + 8)(7k + 9) = 49k^2 + 63k + 56k + 72.
Notice that both 49k^2 and 63k are divisible by 7. This leaves 72: dividing 72 by 7 leaves remainder 2, so there's your answer.
1 is sufficient.
2. t^2 = 7k + 1 means that t^2 + 5t + 6 = 7k + 1 + 5t + 6 = (7k + 7) + 5t.
7k + 7 is obviously divisible by 7, but you can't say anything about 5t, since you don't have any extra info about t.
2 is not sufficient.
Answer A
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Gmat Prep Remainder problem
Source: Beat The GMAT — Data Sufficiency |
