For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by :
- (a) 7 and 11 only
- (b) 11 and 13 only
- (c) 7 and 13 only
- (d) 7, 11 and 13 ✓ UPSC's answer
Why the answer is (d)
• XYZXYZ = XYZ × 1000 + XYZ = XYZ × 1001.
• 1001 = 7 × 11 × 13.
• So every number of this form is divisible by 7, 11 and 13, whatever the digits X, Y and Z.
• Hence option (d).
Why the other options are wrong
- (a) 7 and 11 only
- Option (a) is incorrect because it omits 13, which is also a factor of 1001.
- (b) 11 and 13 only
- Option (b) is incorrect because it omits 7, which is also a factor of 1001.
- (c) 7 and 13 only
- Option (c) is incorrect because it omits 11, which is also a factor of 1001.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.