Question
Download Solution PDFA four-digit pin, say abcd, of a lock has different non-zero digits. The digits satisfy b = 2a, c = 2b, d = 2c. The pin is divisible by ________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A four-digit pin, say abcd, of a lock, has different non-zero digits.
The digits satisfy b = 2a, c = 2b, d = 2c.
Calculation:
c = 2b
⇒ c = 2 × 2a = 4a ...(1)
d = 2c
⇒ d = 2 × 4a = 8a ....(2)
Now, the pin
⇒ abcd = 1000 × a + 100 × b + 10 × c + 1 × d
⇒ abcd = 1000 × a + 100 × 2a + 10 × 4a + 1 × 8a
⇒ abcd = 1000a + 200a + 40a + 8a
⇒ abcd = 1248a
⇒ abcd = (78 × 16)a
⇒ abcd = ((2 × 3 × 13) × 16)a
Hence, the pin is divisible by 2, 3, 13.
∴ The pin is divisible by 2, 3, 13.
Last updated on Jul 17, 2025
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