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If \(x, a,\) and \(b\) are positive integers such that when \(x\) is divided by \(a,\) the remainder is \(b\) and when \(x\) is divided by \(b,\) the remainder is \(a-2,\) then which of the following must be true?
A. \(a\) is even
B. \(x+b\) is divisible by \(a\)
C. \(x-1\) is divisible by \(a\)
D. \(b=a-1\)
E. \(a+2=b+1\)
Answer: D
Source: GMAT Club Tests
A. \(a\) is even
B. \(x+b\) is divisible by \(a\)
C. \(x-1\) is divisible by \(a\)
D. \(b=a-1\)
E. \(a+2=b+1\)
Answer: D
Source: GMAT Club Tests
