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If \(x\) and \(y\) are consecutive positive integers such that \(x < y,\) which of the following statements is true without any exceptions?
I. \((x+1)(y-1) = xy\)
II. \((x+y)^2\) leaves a remainder of \(1\) when divided by \(8.\)
III. The difference between the larger number and the sum of the remainders when \(x\) and \(y\) are divided by each other is \(1.\)
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
Answer: D
Source: e-GMAT
I. \((x+1)(y-1) = xy\)
II. \((x+y)^2\) leaves a remainder of \(1\) when divided by \(8.\)
III. The difference between the larger number and the sum of the remainders when \(x\) and \(y\) are divided by each other is \(1.\)
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
Answer: D
Source: e-GMAT
