Data Sufficiency

swerve wrote: ↑

Wed Jun 02, 2021 3:47 pm

In a certain first grade classroom, the average height is \(x\) inches for the \(5\) girls and \(y\) inches for the \(8\) boys. What is the average height for the \(13\) students in the classroom combined?

1) \(15x+24y=1755\)
2) \(x < 40\)

The OA is A

Source: Veritas Prep

Target question: What is the average height for the 13 students in the classroom combined?

Given: The average height is x inches for the 5 girls and y inches for the 8 boys.
This is a good candidate for rephrasing the target question.

We can think of this is a weighted averages question. So, we'll apply the following formula:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
So, Average weight of classroom = (5/13)(x) + (8/13)(y)
= 5x/13 + 8y/13
= (5x + 8y)/13
So, we can REPHRASE the target question...
REPHRASED target question: What is the value of (5x + 8y)/13?

Statement 1: 15x + 24y = 1755
Notice that we have (5x + 8y) "hiding" in the above equation.
Take 15x + 24y = 1755 and factor the left side to get: 3(5x + 8y) = 1755
Divide both sides by 3 to get: 5x + 8y = 585
So, (5x + 8y)/13 = (585)/13 = 45
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x < 40
No information about y, which means there's no way to determine the value of (5x + 8y)/13
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A