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
I am having a very difficult time with these remainder type questions. Any help would be appreciated. Please explain!
Highlight for OA: A
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Number property question...help
This topic has expert replies
-
jayhawk2001
- Community Manager
- Posts: 789
- Joined: Sun Jan 28, 2007 3:51 pm
- Location: Silicon valley, California
- Thanked: 30 times
- Followed by:1 members
x / 11 yields y as quotient and 3 as remainder. So,
x = 11y + 3
Similarly, x/19 yields (say) z as quotient and 3 as remainder. So,
x = 19z + 3
Equating to x, we get
11y + 3 = 19z + 3
11y = 19z
We know that y and z are integers (as they are quotients).
y = 19z/11
which implies that z has to be a multiple of 11
So, y/19 = z/11 and since z is a multiple of 11, it yields 0 remainder
Hence A
x = 11y + 3
Similarly, x/19 yields (say) z as quotient and 3 as remainder. So,
x = 19z + 3
Equating to x, we get
11y + 3 = 19z + 3
11y = 19z
We know that y and z are integers (as they are quotients).
y = 19z/11
which implies that z has to be a multiple of 11
So, y/19 = z/11 and since z is a multiple of 11, it yields 0 remainder
Hence A
