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Maximizing Algebraic Expression

XAT 2013 · Quantitative Ability & Data Interpretation · Medium · Algebra

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p, q and r are three non-negative integers such that p+q+r=10p + q + r = 10. The maximum value of pq+qr+pr+pqrpq + qr + pr + pqr is

  1. A.

    ≥40 and <50\ge 40 \text{ and } < 50

  2. B.

    ≥50 and <60\ge 50 \text{ and } < 60

  3. C.

    ≥60 and <70\ge 60 \text{ and } < 70

  4. D.

    ≥70 and <80\ge 70 \text{ and } < 80

  5. E.

    ≥80 and <90\ge 80 \text{ and } < 90

Answer

C

Explanation

To maximize product terms, make p,q,rp, q, r as close as possible. For sum = 10, choose integers {3, 3, 4}. pq+qr+pr+pqr=3(3)+3(4)+3(4)+3(3)(4)=9+12+12+36=69pq + qr + pr + pqr = 3(3) + 3(4) + 3(4) + 3(3)(4) = 9 + 12 + 12 + 36 = 69. 69 lies in ≥60 and <70\ge 60 \text{ and } < 70.

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