Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
The question seems forbidding, but start by grabbing onto the most concrete part, which comes at the end.
Start with distributing (x – p1)(x – p2).
(x – p1)(x – p2) = x2 – (p1 + p2)x + p1p2
All we care about is the coefficient of the x term, which is –(p1 + p2). Specifically, we care about the absolute value of this, which is p1 + p2, since primes are by definition positive.
So what we are really asked for is the smallest possible value of p1 + p2, under two conditions:
1) These two primes are consecutive, meaning that there’s no other prime between them.
2) |p1 – p2| > 2, meaning that the primes are more than 2 units apart on the number line.
In other words, the question really is “what is the smallest possible sum of two consecutive primes that are more than 2 units apart?”
Now take the first several primes: 2, 3, 5, 7, 11, 13. The first pair of consecutive primes more than 2 units apart is {7, 11}. Their sum is 18.
The correct answer is D.