## Statistics And Sets Problems

##### This topic has expert replies
Legendary Member
Posts: 1983
Joined: 29 Oct 2017
Followed by:6 members

### Statistics And Sets Problems

by swerve » Wed Jun 02, 2021 3:47 pm

00:00

A

B

C

D

E

## Global Stats

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

### GMAT/MBA Expert

GMAT Instructor
Posts: 15628
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1266 members
GMAT Score:770

### Re: Statistics And Sets Problems

by [email protected] » Thu Jun 03, 2021 5:04 am

00:00

A

B

C

D

E

## Global Stats

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