W, X, Y and Z are four different positive integers. When X is divided

Question

W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X – 4, which of the following is a possible value of X?

I. 6
II. 7
III. 8

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

rajatchopra1994 · Answer

Explanation:
X = YZ + W
if W = X – 4, 
So, X=YZ + X - 4
YZ = 4
case 1: Y = 1 and Z = 4 (Not possible)

case 2: Y = 4 and Z = 1
means when X is divided by 4, the quotient is 1 and the remainder is W

I. X = 6, then W=2 yes
II. X = 7, then W=3 yes
III. X = 8, then W=0 , Not possible as W, X, Y and Z are four different positive integers

IMO-C

Kinshook · Answer

Given: W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. 
Asked: If W = X – 4, which of the following is a possible value of X?

X = Z Y + W = Z Y + X - 4
ZY = 4
X = 4 + W; W<4
4< X < 8

I. 6; 6= 1*4 + 2; YES
II. 7; 7 = 1*4 + 3; YES
III. 8; NO

IMO C

tryingtoaimhigher · Answer

Hi all

Sorry in the explanation above, I did not understand this step:

X = 4 + W; W<4

Would be grateful if someone could explain how to solve this problem. Thanks

A_Nishith · Answer

Given: W, X, Y and Z are four different positive integers. 
When X is divided by Y, the quotient is Z and the remainder is W.
Asked: If W = X – 4, which of the following is a possible value of X?

X = Z Y + W = Z Y + X - 4
ZY = 4
X = 4 + W; W<4
4< X < 8

I. 6; 6= 1*4 + 2; YES
II. 7; 7 = 1*4 + 3; YES
III. 8; NO

Answer: C

BrushMyQuant · Answer

W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W

Dividend = Divisor * Quotient + Remainder

=> X = Y*Z + W

W = X - 4
=> X = YZ + X - 4
=> YZ = 4

I. 6 
=> X = 6, W = 6 - 4 = 2
YZ = 4, Y = 1, Z = 4
All are different positive integers
=>   POSSIBLE

II. 7 
 => X = 7, W = 7 - 4 = 3
YZ = 4, Y = 1, Z = 4
All are different positive integers
=>   POSSIBLE

III. 8 
 => X = 8, W = 8 - 4 = 4
YZ = 4, Y = 1, Z = 4,   NOT POSSIBLE   as Z = W
 YZ = 4, Y = 2, Z = 2,   NOT POSSIBLE   as Y = Z 
 YZ = 4, Y = 4, Z = 1,   NOT POSSIBLE   as Y = W 
=>   NOT POSSIBLE

So,  Answer will be C 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

W, X, Y and Z are four different positive integers. When X is divided

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