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You might fall for the trap answer, D. You’ll break down 156 into 13 times 12 (and realize that you can’t break 13 down any further so there’s no other way to recombine the prime factors to find consecutive integers with a prime), and note that b has to be 13 and a has to be 12. So choice A is, indeed, sufficient. And then when you get to statement 2 you’ll think – yeah, freebie. 13 is bigger than 12, so it has to be 13. But wait – why can’t it be -12 while a is -13? You’ve fallen into the trap – you assumed negative! Woe is you…why do you keep falling for these traps?!
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Re: The product of consecutive integers a and b is 156. What is the value [#permalink]
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15 Feb 2017, 16:22
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Bunuel wrote:
The product of consecutive integers a and b is 156. What is the value of b?
(1) b is prime
(2) b > a
We are given that the product of consecutive integers a and b is 156. If we let a = x and b = x + 1 (or vice versa), we can create the following equation:
x(x + 1) = 156
x^2 + x - 156 = 0
(x + 13)(x - 12) = 0
x = -13 or x = 12
Thus, in no particular order, a and b could be -13 and -12 or 12 and 13. We must determine the value of b.
Statement One Alone:
b is prime.
Since no negative numbers can be prime and 12 is not a prime, the only possible value of b is 13. Statement one alone is sufficient to answer the question.
Statement Two Alone:
b > a
Using the information in statement two, b could be 13 or -12. Statement two is not sufficient to answer the question.
Answer: A
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