Number Property

[artstudent]

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


Is there another way to evaluate statement 2 using number properties?

[Anurag@Gurome]

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

If w, x, and y are consecutive integers then y = x + 1 = w + 2

Statement 1: y = w + 2
As x is an integer and w < x < y, x must be equal to (w + 1) = (y - 1)
Thus, w, x, and y are consecutive integers.

Sufficient

Statement 2: (w + x + y)/3 = x ---> (w + y) = 2x
This means w, x, and y are uniformly distributed integers. They may or may not be consecutive integers.

Not sufficient

The correct answer is A.

[sl750]

Although we don't know what x is in statement 1, we know that it is between w and y. Can you give an example of where this condition is satisfied and three numbers are not consecutive?

[Anurag@Gurome]

Although we don't know what x is in statement 1, we know that it is between w and y. Can you give an example of where this condition is satisfied and three numbers are not consecutive?

Thank you for pointing that out. I've missed the fact that x is an integer and it lies between w and y. Statement 1 is indeed sufficient.
Editing my reply.

[saketk]

Since all the numbers are integer -- using condition 1 we will get the answer-- Hence A is sufficient.
For condition B - Lets take 1,2,3 = mean 2.. also for 1,3,5 mean is 3. Hence the condition is not suffiencent.

A should be the right answer.

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


Is there another way to evaluate statement 2 using number properties?

[gmatdriller]

statement (2) reduces to x = (w+y)/2...as stated by Anurag
we know that average of 2 numbers is also the mid-point
w.......x.........y
w any y can be any number and x is their mid-point.
1,2,3 satisfies (2) and they are consecutive.
Although 1,3,5 also satisfies (2), they are not consecutive.
Insufficient.

[navami]

statement 1 sufficient .
statement 2 insufficient becaz
-1, 1, 3 will satisfy (2) but they are not consecutive but 1, 2, 3 will also satisfy where as they are consecutive,