If w, x and y are integers such that w

Question

If w, x and y are integers such that w < x < y, are w, x and y consecutive integers?

(1) y - w = 2

(2) The average (arithmetic mean) of w, x and y is x

Bunuel · Answer

If w, x and y are integers such that w < x < y, are w, x and y consecutive integers?

(1) y - w = 2 --> y = w + 2. Thus we have that w < x < (w + 2). There is only one integer between w and w + 2, which is w + 1. Thus the three integers are w, x = w + 1, and y = w + 2 --> w, x and y are constitutive integers. Sufficient.

(2) The average (arithmetic mean) of w, x and y is x. If w=0, x=5 and y=10, then the answer is NO but if w=0, x=1 and y=2, then the answer is YES. Not sufficient.

Answer: A.

Hope it's clear.

ShashwatPrakash · Answer

Hi  Bunuel ,

I understand the no. approach for St.2, but I don't understand what I am doing wrong.

I assumed that the nos. are consecutive. Let w=n, so x=n+1 and y=n+2
The avg of three no. would be  / = n+1, which is equal to x, same as St.2, so the assumption is correct.

Kindly explain.

Bunuel · Answer

You sowed that (2) is true for consecutive integers but what if (2) is also true if the integers are not consecutive? In this case you'd get an YES and a NO answer to the question.

bumpbot · Answer

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If w, x and y are integers such that w < x < y, are w, x and

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