If the 5- digit number 676xy is divisible by 3, 7, and 11 then what is the value of (3x - 5y)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 9
As the number is divisible by 3, 7, 11 so the number will also be divisible by the LCM of 3, 7, 11
⇒ LCM(3, 7, 11) = 231
We need to find a multiple of 231 near the number 676xy.
By hit and trial,
⇒ 231 × 300 = 69300
Now we need to find a multiple bit lower than 300
⇒ 231 × 293 = 67683
Here, x = 8, and y = 3
⇒ (3x - 5y) = 3(8) - 5(3)
⇒ 24 - 15 = 9