What number is 6 more than x + y ?

[BTGModeratorVI]

What number is 6 more than x + y ?

(1) y is 3 less than x.
(2) y is twice x.

Answer: C
Source: Official Guide

[Jay@ManhattanReview]

What number is 6 more than x + y ?

(1) y is 3 less than x.
(2) y is twice x.

Answer: C
Source: Official Guide

So, we have to calculate the value of x + y + 6.

Let's take each statement one by one.

(1) y is 3 less than x.

y = x – 3. We can't get the value of x + y + 6. Insufficient.

(2) y is twice x.

y = 2x. We can't get the value of x + y + 6. Insufficient.

(1) and (2) together

From y = x – 3 and y = 2x, we get x = – 3 and y = – 6; thus, x + y = 6 = – 3 – 6 + 6 = –3. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

What number is 6 more than x + y ?

(1) y is 3 less than x.
(2) y is twice x.

Answer: C
Source: Official Guide

Target question: What is the value of x + y + 6?

Statement 1: y is 3 less than x.
We can write: y = x - 3
There are several values of x and y that satisfy this equation. Here are two:
Case a: x = 3 and y = 0. In this case, the answer to the target question is x + y + 6 = 3 + 0 + 6 = 9
Case b: x = 4 and y = 1. In this case, the answer to the target question is x + y + 6 = 4 + 1 + 6 = 11
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is twice x.
We can write: y = 2x
There are several values of x and y that satisfy this equation. Here are two:
Case a: x = 1 and y = 2. In this case, the answer to the target question is x + y + 6 = 1 + 2 + 6 = 9
Case b: x = 2 and y = 4. In this case, the answer to the target question is x + y + 6 = 2 + 4 + 6 = 12
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that y = x - 3
Statement 2 tells us that y = 2x
We have 2 DIFFERENT linear equations with 2 variables.
Since we COULD solve the system for x and y, we COULD determine the value of x + y + 6
ASIDE: Although we COULD solve the system of equations, we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.

Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent