Hi,
Answer has to be “E”.
There is not much information about “x”
Given:
x, y > 0 and integers
y < 5x
z = Rem When 5x is divided y.
Question: Value of “z”?
Statement I is insufficient:
When y+1 is divided by 5, the remainder is 1
i.e., y+1 could be 1,6, 11, 16, …..
So “y” values could be 0,5,10,15,20,25…(“y” can’t be zero as it is given y is positive).
Given y < 5x
Let’s say,
x = 7 and y = 5
then “y” is less than 5 < 35
then z = 0
But if
x = 7 and y = 15
then “y” is still less than 15 < 35
But we get different z, i.e., z = 5
So different values of “z”. Not sufficient.
Statement II is insufficient.
When y+1 is divided by 4, the remainder is 2.
Similar to statement I,
y+1 could be 2,6, 10, 14,18 …..
So “y” values could be 1,5,9,13,17,21,25…(“y” can’t be zero as it is given y is positive).
Given y < 5x
Let’s say,
x = 7 and y = 5
then “y” is less than 5 < 35
then z = 0
But if
x = 7 and y = 9
“y” is still less than 9 < 35
But z = 8
So different values of “z”. Not sufficient.
Together still insufficient:
Values could be still,
x = 7 and y = 5
then “y” is less than 5 < 35
then z = 0
OR
x = 7 and y = 5
then “y” is less than 5 < 35
then z = 0
x = 7 and y = 25
then “y” is less than 25 < 35
then z = 10
Still we are getting different values of “z”.
Together still not sufficient.
So the answer is E.
Hope this helps
_________________
GMAT Mentors