2018 · Q17
Consider the following statements in respect of three 3-digit numbers XYZ, YZX and ZXY:
- 1The sum of the numbers is not divisible by (X + Y + Z).
- 2The sum of the numbers is divisible by 111.
Which of the above statements is/are correct ?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
XYZ + YZX + ZXY = 100(X+Y+Z) + 10(X+Y+Z) + (X+Y+Z) = 111(X + Y + Z). This is clearly divisible by (X + Y + Z), so statement 1 is false, and it is visibly divisible by 111, so statement 2 is true. Hence option B.