If the 7 -digit number x8942y4 is divided by 56, whatis the value of ( x2 + y) for the largest value of y, where x and y are natural numbers ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 55
Concept used :
1. Divisibility of 7 - The difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0.
2. Divisibility of 8 - If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.
Solution :
Given that a 7-digit number is divisible by 56 which means it is divisible by both 7 and 8.
For the number to be divisible by 8, 2y4 should be divisible by 8.
Therefore y = 6, 264 is divisible by 8.
Now, x894264 is dic=visible ny 7
If we take x = 7, the number is divisible by 7.
Hence required value = (x2 + y) =(72 + 6) = 49 + 6 = 55