If p, q, r, and s are consecutive integers, with

This topic has expert replies
Legendary Member
Posts: 2276
Joined: Sat Oct 14, 2017 6:10 am
Followed by:3 members
If p, q, r, and s are consecutive integers, with p<q<r<s, is pr<qs?

(1) pq<rs

(2) ps<qr

The OA is A.

I got confused with the inequalities. Experts, can you show me how you'd solve it? Please.

User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 am
Location: Boston, MA
Thanked: 1153 times
Followed by:128 members
GMAT Score:770

by DavidG@VeritasPrep » Thu Mar 15, 2018 10:37 am
VJesus12 wrote:
If p, q, r, and s are consecutive integers, with p < q < r < s, is pr < qs?

(1) pq < rs

(2) ps < qr

The OA is A.

I got confused with the inequalities. Experts, can you show me how you'd solve it? Please.
Interesting question. We could do a little algebra here. If the numbers are consecutive, and p is the smallest, we can designate the other values as p + 1, p + 2, and p + 3.

Our rephrased question: Is p(p +2) < (p+1)(p+3)?
Simplify: p^2 + 2p < p^2 +4p + 3?
2p < 4p + 3?
-2p < 3?
Is p > -3/2?

Statement 1 rephrased: p(p+1) < (p+2)(p+3)
p^2 + p < p^2 +5p + 6
p < 5p + 6
-4p < 6
p> -6/4
p > -3/2 --> that's exactly what we were trying to determine! Statement 1 alone is sufficient to answer the question.

Statement 2 rephrased: p(p+3) < (p+1)(p+2)
p^2 + 3p < p^2 +3p + 2
0 < 2.
We already know that. Not sufficient.

The answer is A
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course