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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If p, q, r, and s are consecutive integers, with tagged by: VJesus12 ##### This topic has 1 expert reply and 0 member replies ## If p, q, r, and s are consecutive integers, with If p, q, r, and s are consecutive integers, with p (1) pq (2) ps The OA is A. I got confused with the inequalities. Experts, can you show me how you'd solve it? Please. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply 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

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