Question : A six-digit number 763254 is divisible by 18. If we subtract five times of 41 from the number, then the new number which is formed will be divisible by:
Option 1: 2
Option 2: 7
Option 3: 5
Option 4: 3
Correct Answer: 7
Solution :
Given: The number 763254 is divisible by 18.
5 times of 41 from the number is subtracted = 763254 – 5 × 41 = 763254 – 205 = 763049
Now, Using divisibility rules:
For 2, if its last digit is even.
For 3, if the sum of its digits is divisible by 3 = 7 + 6 + 3 + 0 + 4 + 9 = 29
For 5, if its last digit is 0 or 5.
For 7, multiply the last digit by 2, and subtract it from the rest of the number; if the result is divisible by 7 = 76304 – 2 × 9 = 76304 – 18 = 76286, which is divisible by 7.
So, the number is divisible by 7.
Hence, the correct answer is 7.
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