Tough DS Questions

[Vaibhav Sinha]

Q. For integers a and b, if (a^3 – a^2 – b)^1/2 = 7, what is the value of a?

(1) a^2 - a = 12

(2) b^2 - b = 2

OA B

[Jammie Peng]

(a^3 – a^2 – b)^1/2 = 7 can be simplified to a^3 – a^2 = 49 + b or b = a * (a^2 - a) - 49

(1) a^2 - a = 12 evaluated will give a = 4 or a = -3.  If you plug into the previous equation b = a * (a^2 - a) - 49 above, you will get 2 sets of answers: (a = 4 and b = -1) OR (a = -3 and b = 85).  Since there are 2 possible answers for a, this is NOT SUFFICIENT

(2) b^2 - b = 2 evaluated will give b = 2 or b = -1.  If you plug into the previous equation a^3 – a^2 = 49 + b above, you get a^2 * (a - 1) = 51 or a^2 * (a - 1) = 48.  The first equation will not give an integer for a since 51 = 3 * 17, which cannot fit into a * (a^2 - a).  The second equation will give a = 4 since 48 = 4 * 4 * 3.  Since this only 1 answer for a, this is SUFFICIENT

Therefore, the answer is B: (2) alone is sufficient but (1) alone is not sufficient.

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