How many ways can N students sit in a row of N seats at a movie? (1)

Question

How many ways can N students sit in a row of N seats at a movie?

(1) N^2 = 7N + 18

(2) N is odd

TestPrepUnlimited · Answer

The answer in terms of N is N!, so we want to know N for sufficiency.

Statement 1:

N^2 - 7N - 18 = 0  and  (N - 9)(N+2) = 0 . The only meaningful solutions is N = 9 so sufficient.

Statement 2:

Insufficient.

Ans: A

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

This should be C, right? The first equation factors into multiple solutions:

N^2-7N-18=0

(N-9)(N + 2) = 0

N = 9 or N = -2

The second qualifies that only the odd value, 9, counts, so both statements together are sufficient. But wait – do we really know that neither alone is sufficient? Could we have a negative number of students? That’s impossible; -2 students could never attend a movie together. So  statement 1 alone is sufficient  – C was the trap here, making you think that you needed both statements. But knowing that an “easy C” is often a trap, you should be aware of that. And as a strategic point, being aware of that trap can help you on questions with tougher math involved.

If C seems too good to be true, it probably is; reconsider the statements, particularly if one clearly gives more information than the other.

How many ways can N students sit in a row of N seats at a movie? (1)

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