If the 5-digit number 538xy is divisible by 3, 7, and 11, then the value of (x2 + y2) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 13
Given that the 5-digit number 538xy is divisible by 3, 7, and 11.
So we will first evaluate: LCM (3, 7, 11) = 231
The largest possible value of 538xy is 53899
When we divide 53899 by 231 we obtain 76 as the remainder.
So,
Required number = 53899 – 76 = 53823
Hence,
x = 2 and y = 3
⇒ (x2 + y2) = 4 + 9 = 13