The Quest for 700: Weekly GMAT Challenge (Answer)

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 (xp1)(xp2).
(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) |p1p2| > 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.

onTrack by mbaMission

A first-of-its-kind, on-demand MBA application experience that delivers a personalized curriculum for you and leverages interactive tools to guide you through the entire MBA application process.

Get Started!

Upcoming Events

Upcoming Deadlines

  • Berkeley Haas (Round 1)

Click here to see the complete deadlines

2024–2025 MBA Essay Tips

Click here for the 2023–2024 MBA Essay Tips

MBA Program Updates

Explore onTrack — mbaMission’s newest offering allowing you to learn at your own pace through video. Learn more