If x and y are positive integer, what is the remainder when x is divided by y ?
(1) When x is divided by 2x, the remainder is 4.
(2) When x + y is divided by y, the remainder is 4.
x=yn+r. Question is r=?
(1) This statement is clearly insufficient, no info about y.
Maybe there is a typo? If it were: "When x is divided by 2y
, the remainder is 4." It would make more sense, though still would be insufficient.
But still let's consider this case too:x=2yk+4
. x=20 y=8 --> x/2y=20/16 remainder 4 and x/y=20/8 remainder also 4
, BUT x=10 y=3 --> x/2y=10/6 remainder 4 and x/y=10/3 remainder 1
. Two different remainders: not sufficient.
(2) x+y=yp+4 --> x=y(p-1)+4 --> this statement directly gives a remainder of 4 upon dividing x by y. Sufficient.
Look at the red coloured equation above.
=> x divided by y has a remainder of 4. Is my understanding correct?
2nd query: For first equation (the red one mentioned above) x= 2yk + 4, you solved it by plugging in the numbers while for second correct equation x= y(p-1) + 4 you didn't solve it by plugging the numbers. Why did you not plug the numbers in equation 2? I mean how did you find out without counter checking that equation 2 will be true for all positive integers???