2020 · Q43
Let XYZ be a 3-digit number. Let S = XYZ + YZX + ZXY. Which of the following statements is/are correct?
- 1S is always divisible by 3 and (X + Y + Z)
- 2S is always divisible by 9
- 3S is always divisible by 37
Select the correct answer using the code given below:
Elementary MathematicsNumber System
- A1 only
- B2 only
- C1 and 2
- D1 and 3
Explanation
XYZ + YZX + ZXY = 111(X + Y + Z) = 3 × 37 × (X + Y + Z). So S is divisible by 3, by (X + Y + Z), and by 37. But 111 = 3 × 37 is not a multiple of 9, so statement 2 is false. Statements 1 and 3 hold.