Source: - Manhattan GMAT (www.manhattangmat.com)
w, x, y, and z are integers. If w > x > y > z > 0, is y a common divisor of w and x?
(1)w/x = z^-1 + x^-1
(2)w^2-wy-2w=0
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Manhattan GMAT challenge question
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ratindasgupta
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Statement 1 - w/x = z^-1 + x^-1
Solving it, we get that wz = x + z
Since all 4 are integers, we can deduce that z = 1 and w is greater than x by 1. Since x is 1, y will have to be 2 or more. So y cannot be a factor of w and x which are consecutive numbers. SUFF
2. w^2-wy-2w=0
Solving this, we get, w - y = 2
So w , x and y have to be consecutive integers. So y cannot be a factor of w and x. SUFF
Answer should be D
Solving it, we get that wz = x + z
Since all 4 are integers, we can deduce that z = 1 and w is greater than x by 1. Since x is 1, y will have to be 2 or more. So y cannot be a factor of w and x which are consecutive numbers. SUFF
2. w^2-wy-2w=0
Solving this, we get, w - y = 2
So w , x and y have to be consecutive integers. So y cannot be a factor of w and x. SUFF
Answer should be D
