When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3. What is the remainder when y is divided by 19? A. 0B. 1C. 2D. 3E. 4

A) 0

Step-by-step explanation:

When x is divided by 11, we have a quotient of y and a remainder of 3

x/11 = y + 3

x = 11y + 3 ... (1)

When x is divided by 19, we have a remainder of 3 also

x/19 = p + 3 (p = quotient)

x = 19p + 3 ... (2)

Equate (1) and (2)

x = 11y + 3 = 19p + 3

11y + 3 = 19p + 3

11y = 19p + 3 - 3

11y = 19p

Divide both sides by 11

11y/11 = 19p/11

y = 19p/11

y and p are integers. 19 is a prime number. P/11 is also an integer

y = 19 (integer)

This implies that y is a multiple of 19. When divided by 19, there is no remainder. The remainder is 0