2 points If the 5-digit number 776xy is divisible by 3, 7 and 11, then the value of (5x+3y)? O A. 13 MI DUAL CAMERA REDMI NOTE 5 PRO O B.21 O C. 23 O D. 26 O Other:
Answers
Value of 5x + 3y is 23 if 5-digit number 776xy is divisible by 3, 7 and 11,
Given:
776xy is 5-digit number
Number is divisible by 3, 7 and 11
To Find:
Value of 5x + 3y
Solution:
A number is divisible by 3 is sum of digits is divisible by 3
A number is divisible by 11 if difference of sum of even digits and odd digits is divisible by 11
776xy
Sum of digits = 7 + 7 + 6 + x + y
= 20 + x + y
Hence Divisible by 3 if
x + y = 1 , 4 , 7 , 10 , 13 , 16 ,
776xy
(7 + 6 + y) - (7 + x)
= 6 + y - x
Divisible by 11 if 6 + y - x = 0 or 11
y - x = -6 , y - x = 5
x = y + 6 or y= x + 5
Solving both possible solutions are :
x = 8 , y = 2
x = 1 , y = 6
x = 4 , y = 9
77682 Not Divisible by 7
77616 Divisible by 7
77649 Not Divisible by 7
77616 is Divisible by 7
x = 1 and y = 6
5x + 3y
= 5(1) + 3(6)
= 5 + 18
=23
Correct option is C) 23
Value of 5x + 3y is 23 if 5-digit number 776xy is divisible by 3, 7 and 11,
Given :
776xy is a 5-digit number
To Find :
The value of (5x+3y)
Solution :
If a five digit number is divisible by 3, 7 and 11, then we can say that it can also be divisible by (3×7×11 = 231).
Let us assume, 77699 be the greatest possible value
Now,
On dividing 77699 by 231, we get 336.359
So, the actual number is (231 × 336) = 77616
Hence, x = 1 and y = 6
∴ 5x + 3y
= 5×(1) + 3×(6)
= 5 + 18
= 23
Therefore, the value of (5x + 3y) is 23.