When the positive integer x is divided by 11

VJesus12 wrote: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. 0
B. 1
C. 2
D. 3
E. 4

A fast approach is to find a value of x that meets the given conditions.

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....
Notice that x = 3 meets the above conditions.
3 divided by 11 = 0 with remainder 3. In this case, y = 0
Likewise, 3 divided by 11 also leaves a remainder of 3

What is the remainder when y is divided by 19?
In the above example, y = 0
So, when we divide 0 by 19, the remainder is 0

Answer: A

Cheers,
Brent

Hi VJesus12,

We're told that...
X/11 = Y remainder 3
X/19 = something remainder 3

With the first piece of information, we know that X is 3 greater than a multiple of 11; with the second piece of information, we know that X is 3 greater than a multiple of 19. To have a remainder of 3 when you divide X by BOTH 11 and 19, X must be a number that is 3 greater than a MULTIPLE of BOTH 11 and 19.

We're asked what the remainder would be when Y is divided by 19. At this point, you might recognize that you could choose Y=19 and solve from there. If you don't recognize why that that relationship exists, then here's a more step-heavy way to get to the correct answer:

X = (11)(19) + 3 = 209 + 3 = 212

212/11 = Y remainder 3
212 = 11Y + 3
209 = 11Y
209/11 = Y
19 = Y

We're ultimately asked what the remainder would be when 19 is divided by 19. The remainder is 0.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich