If x and y are positive integers and y<5x, the remainder is z when 5x

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