Consider a 6 digit number of the form XYXYXY The number is divisible by ........

Quantitative Aptitude (CDS) Number System

Consider a 6-digit number of the form XYXYXY. The number is divisible by :

This questions was previously asked in

2023 CDS -1 MATH

3 and 7 only

7 and 13 only

3, 13 and 37 only

3, 7, 13 and 37

Let’s analyze a 6-digit number XYXYXY:

- It can be written as: 100000X + 10000Y + 1000X + 100Y + 10X + Y = X(100000+1000+10) + Y(10000+100+1) = X(101010) + Y(10101)

- So, the general form is 101010X + 10101Y.

- 101010 = 2 × 5 × 10101, and 10101 = 3 × 7 × 13 × 37.

- Thus, any number of the form XYXYXY is divisible by 10101 (since Y is multiplied by it), so by 3, 7, 13, and 37.

Let’s check each option:

- Option 1: 1, 3 and 7 only – Not complete.

- Option 2: 2, 7 and 13 – Missing 3 and 37.

- Option 3: 3, 13 and 37 only – Missing 7.

- Option 4: 3, 7, 13 and 37 – Contains all divisors.

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