BTGmoderatorLU wrote: ↑Thu Sep 02, 2021 8:39 am
Source: Veritas Prep
What is the value of x + y?
1) 7x + 3y + 6z = 16
2) 3x + 5y = 3z + 5
The OA is
C
Great question!
Target question: What is the value of x + y?
Statement 1: 7x + 3y + 6z = 16
Notice that, since we have the 3rd variable, z, we can assign ANY values to x and y and then simply make the z-value such that the equation holds true.
For example, if we let x = 0 and y = 0, then we get 0 + 0 + 6z = 16. So, z = 16/6. In this case,
x + y = 0 + 0 = 0
Similarly, if we let x = 1 and y = 1, then we get 7 + 3 + 6z = 16. So, z = 6/6. In this case,
x + y = 1 + 1 = 2
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3x + 5y = 3z + 5
We can apply the same logic that we used for statement 1 to show that statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that
7x + 3y + 6z = 16
Statement 2 tells us that
3x + 5y = 3z + 5
IMPORTANT: Many students will assume that, since we have a system of 3 equations with 2 variables, then we cannot answer the target question.
This would be a correct assumption
IF the target question asked for the
individual values of x and y.
HOWEVER, notice that the target question only asks for the
sum of x and y.
This we might be able to find.
First, take
3x + 5y = 3z + 5 and subtract 3z from from both sides to get:
3x + 5y - 3z = 5
Then multiply both sides by 2 to get:
6x + 10y - 6z = 10
We now have:
7x + 3y + 6z = 16
6x + 10y - 6z = 10
ADD the equations to get:
13x + 13y = 26
Divide both sides by 13 to get:
x + y = 2
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
