If the 9 digit number 5p42978n6 is divisible by 72 what is the value of 2p 1 where n is the second l...........

Quantitative Aptitude (CHSL) Number series

If the 9-digit number 5p42978n6 is divisible by 72, what is the value of (2p - 1), where n is the second largest of all the possible

values of n? Given that p and n are natural numbers.

This questions was previously asked in

SSC CHSL 3rd June 2022 Shift-1

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Explanation:

To solve the problem, we need to consider divisibility by both 8 and 9, as the number is divisible by 72 (which is 8 and 9 together).

- Divisibility by 8: The last three digits, 78n6, must be divisible by 8. Checking through possible values of n (1 to 9), for n = 4, 786 is divisible by 8.

- Divisibility by 9: The sum of digits 5 + p + 4 + 2 + 9 + 7 + 8 + 4 + 6 must be divisible by 9. This simplifies to p + 45 + n. Since n = 4 is the second largest, find the smallest p such that the sum is divisible by 9.

- Try different p values until the sum is divisible by 9.

- Value of (2p - 1) is required.

Given options:

- Option 1: 17 - Doesn't work.

- Option 2: 21 - Doesn't work.

- Option 3: 15 - ?? Correct Answer

- Option 4: 11 - Doesn't work.

Hence, the correct choice is Option 3: 15.