If x, y and z are positive integers such that when x is divi

Question

If x, y and z are positive integers such that when x is divided by y, the remainder is z and when x is divided by z, the remainder is (y - 2), then which of the following must be true?
(A) z = (y-1)
(B) (x + z) is divisible by y
(C) (x-1) is divisible by y 
(D) y is even
(E) None of these

Adambhau · Answer

The tough one! My answer is A.

For example: x=5 and y=3, x/y --> Remainder=z=2; x/z=5/2 --> Remainder=1=y-2

So z=2 and y=3, which means z=y-1

This satisfies only option A. I tried different values but can not eliminate the option A.

Abhishek12341234 · Answer

2 also fills up and it is universal true
when x/y |R=z

X+Z must be divisible by y

easy example is 5/2 r=1
5+1 is divisible by 2 try it

DebaGMAT001 · Answer

Tough one.. I don't the answer yet, but looks like option E.

Here is how it goes..

y when divided by x gives remainder z, so we can write equation
 kx = y - z , where k=quotient --------- (I)

when x is divided by z, it gives remainder y-2, so we can write
 kz = x - (y-2) , where k=quotient --------- (II)

if we do (I) + (II), we get:
 k(x+z) = x - (z-2) 
so, we can say if x is divided by (x+z) we get remainder z-2

if we do (I) - (II), we get:
 k(x-z) = 2*(y-1) - (x+z) 
so, we can say if 2*(y-1) is divided by (x-z) we get remainder (x+z)
Alternatively, if (x+z) is divided by (z-x) we get remainder 2(y-1)

In any such case, it does not go with the option choices provided

ndcuong · Answer

If x divided by y leaves a remainder of z, then y > z. And if x divided by z leaves a remainder of y - 2, then z > y - 2. Therefore, we have y > z > y - 2, and since x, y, and z are positive integers z = y - 1. Is this reasoning correct?

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abelka · Answer

I got "A" as an answer. Can someone please clarify where my logic is incorrect?

(1) "when x is divided by y, the remainder is z"
from this, we can write that y>z (remainder is always smaller than the divider)

(2) "when x is divided by z, the remainder is (y - 2)"
from this, we can write that Y-2<Z, or we can rewrite is as Y<Z+2

(1)+(2)
Z<Y<Z+2
but x, y and z are positive integers.
so Y must be equal to Z+1.

Any suggestions why it is wrong?

bumpbot · Answer

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If x, y and z are positive integers such that when x is divi

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