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.
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 15
Divisibility of 8: When the last three digits of a number is divisible by 8, the number is divisibile by 8.
Divisibility of 9: Sum of all the digits of a number is divisible by 9, the nymber is divisible by 9.
According to the given question,
The number 5p42978n6 is divisible by 72 ⇒ The number is divisible by both 8 and 9.
⇒ 8n6 is divisible by 8
⇒ n can be (1, 5, 9)
So, n = 5
Now, sum of digits = (5 + p + 4 + 2 + 9 + 7 + 8 + 5 + 6) = 46 + p
So, p = 8 ⇒ 46 + 8 = 54 which is divisible by 9.
Then, 2p - 1 = 2(8) -1 = 16 - 1 = 15
Hence the required answer is 15.