Data Sufficiency

AbeNeedsAnswers wrote:What number is 6 more than x + y ?

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

C

Source: Official Guide 2020

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

Hi All,

We're asked what number is 6 MORE than (X+Y). This question can be approached in a couple of different ways, including by TESTing VALUES. It's worth noting that the prompt does NOT place any restrictions on X and Y, so they could be positive, negative, 0, fractions, etc.

(1) Y is 3 LESS than X.

IF....
X=3 and Y=0, then the answer to the question is 3+0+6 = 9
X=4 and Y=1, then the answer to the question is 4+1+6 = 11
Fact 1 is INSUFFICIENT

(2) Y is TWICE X.
IF....
X=1 and Y=2, then the answer to the question is 1+2+6 = 9
X=2 and Y=4, then the answer to the question is 2+4+6 = 12
Fact 2 is INSUFFICIENT

Combined, we know...
Y is 3 LESS than X.
Y is TWICE X.

At this point, you might wonder how Y is LESS than X while also being TWICE X. This can happen when the variables are NEGATIVE. We can create the following two equations with the given information:
Y = X - 3
Y = 2X

This is a 'System' of equations (2 variables and 2 unique equations), so we CAN solve for the exact values of X and Y. They are:
2X = X - 3
X = -3
Y = -3 - 3 = -6

Thus, the answer to the question is (-3)+(-6)+6 = -3
Combined, SUFFICIENT

Final Answer: C

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