Aroon’s PIN has four digits. When the first digit (readingfrom the left) is moved to the end of the PIN, the resulting integeris 6 less than 3 times Aroon’s PIN. What could Aroon’s PIN be?
2856
Let’s denote Aroon’s PIN by 1000a + b, where 0 ≤a ≤9 is its first digit and 0 ≤b < 1000 is the three-digit number formed by the remaining digits of his PIN.
When the first digit of Aroon’s PIN is moved to the end, the new number is 10b + a. Hence:
3(1000a + b) − 6 = 10b + a
∴2999a = 7b + 6
Given 0 ≤ b < 1000, we have 6≤ RHS< 7006, hence 0< a < 3, so a must be 1 or 2.
If a =1, we have 7b + 6 =2999, so b =427 4/7 which is not a whole number.
If a = 2, we have 7b + 6 = 5998, so b= 856. We can easily check that 2856 × 3 − 6 = 8562.
Hence Aroon’s PIN must be 2856.
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