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Absolute Value Equation

XAT 2014 · Quantitative Ability & Data Interpretation · Medium · Algebra

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The sum of the possible values of X in the equation ∣X+7∣+∣X−8∣=16|X + 7| + |X - 8| = 16 is:

  1. A.

    0

  2. B.

    1

  3. C.

    2

  4. D.

    3

  5. E.

    None of the above

Answer

B

Explanation

Case 1: X<−7  ⟹  −(X+7)−(X−8)=16  ⟹  −2X+1=16  ⟹  X=−7.5X < -7 \implies -(X+7) - (X-8) = 16 \implies -2X + 1 = 16 \implies X = -7.5. Case 2: −7≤X<8  ⟹  (X+7)−(X−8)=16  ⟹  15=16-7 \le X < 8 \implies (X+7) - (X-8) = 16 \implies 15 = 16 (No solution). Case 3: X≥8  ⟹  (X+7)+(X−8)=16  ⟹  2X−1=16  ⟹  X=8.5X \ge 8 \implies (X+7) + (X-8) = 16 \implies 2X - 1 = 16 \implies X = 8.5. Sum of possible values =8.5−7.5=1= 8.5 - 7.5 = 1.

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