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Number Game Maximum Difference

XAT 2023 · Quantitative Ability & Data Interpretation · Medium · Algebra

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Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

  1. A.

    67

  2. B.

    58

  3. C.

    49

  4. D.

    40

  5. E.

    None of the above

Answer

B

Explanation

Let positive integers be rr and ss. 2r−205+2s−205=16  ⟹  2r+2s−40=80  ⟹  2(r+s)=120  ⟹  r+s=60\frac{2r - 20}{5} + \frac{2s - 20}{5} = 16 \implies 2r + 2s - 40 = 80 \implies 2(r+s) = 120 \implies r + s = 60. Since r,sr, s are positive integers, min value is 1, max is 59. Max difference ∣r−s∣=∣59−1∣=58|r - s| = |59 - 1| = 58.

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