What is the value of (k – w ) + (k – x ) + (k – y )?

[BTGmoderatorAT]

What is the value of (k - w ) + (k - x ) + (k - y )?

(1) w, x, and y are three consecutive odd numbers
(2) The mean of w, x, and y is k

What's the best way to determine which statement is sufficient? Can any experts help?

[ErikaPrepScholar]

Statement 1

We know that w, x, and y are consecutive odd integers, but

• we don't know which integers they are - could be 1, 3, and 5 or 19, 21, and 23

• we don't know anything about k - could be 1 or 5000

We could get a wide range of answers for the value of (k-w) + (k-x) + (k-y) with all of these different numbers. Insufficient.

Statement 2

We know that the average of w, x, and y is k. In other words:
$$\frac{w+x+y}{3}=k$$
which then simplifies to
$$w+x+y=3k$$

We can rearrange our initial equation to give:
$$\left(k-w\right)+\left(k-x\right)+\left(k-y\right)=3k-\left(w+x+y\right)$$
Then substituting 3k for w+x+y gives:
$$3k-3k=0$$

So the value of the expression is 0. Sufficient.

[Brent@GMATPrepNow]

What is the value of (k - w ) + (k - x ) + (k - y )?

(1) w, x, and y are three consecutive odd numbers
(2) The mean of w, x, and y is k

Target question: What is the value of (k - w ) + (k - x ) + (k - y )?
This is a good candidate for rephrasing the target question.

Take: (k - w ) + (k - x ) + (k - y )
Simplify to get: 3k - w - x - y
Rewrite as: 3k - (w + x + y)

REPHRASED target question: What is the value of 3k - (w + x + y) ?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: w, x, and y are three consecutive odd numbers
Since we have no information about k, there's no way to determine the value of 3k - (w + x + y)
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The mean of w, x, and y is k
This tells us that (w + x + y)/3 = k
Multiply both sides by 3 to get: w + x + y = 3k
If w + x + y = 3k, then 3k - (w + x + y) = 3k - (3k) = 0
Perfect, the answer to the REPHRASED target question is 0
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent