There are 300 seniors at Morse High School, and 40% of them

Hi All,

This question can be solved in a variety of ways - with ratios, as a weighted average, or even by TESTing THE ANSWERS. Most Test Takers would probably take an algebraic approach with this question (which is fine), but here's how you can use the answers to your advantage and just do Arithmetic...

We're told a few facts about a group of students:
1) There are 300 seniors and 40% of them own a car.
2) There are X non-seniors and 10% of them own a car.
3) 15% of ALL the students own a car.

We're asked for the total number of NON-seniors at the school.

From a logical standpoint, it would take a LOT more than 300 non-seniors to "bring the average down" from 40% car ownership to 15% car ownership. Given the answer choices that come with this prompt, the correct answer is likely to be one of the larger options.

Let's start with Answer C: 1200....

Seniors with a car: (.4)(300) = 120
Non-seniors w/ a car: (.1)(1200) = 120

Total with a car/All students = 240/1500
15% of 1500 = 225
This answer is NOT a match; as a percent, it is TOO BIG. We need more non-seniors to bring the percent down...

Between Answers D and E, E seems like "easier math"

Answer E: 1500....

Seniors with a car: (.4)(300) = 120
Non-seniors w/ a car: (.1)(1500) = 150

Total with a car/All students = 270/1800
15% of 1800 = 270
This IS a match, so this MUST be the answer.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC wrote:There are 300 seniors at Morse High School, and 40% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 15% of all the students at Morse have cars, how many students are in those other three lower grades?

A. 600
B. 900
C. 1200
D. 1350
E. 1500

OA E

Source: Magoosh

We see that 300 x 0.4 = 120 seniors have cars.

If we let n = the number of students in the remaining grades, then 0.1n have cars. Since 15% of all students have cars:

(120 + 0.1n)/(n + 300) = 0.15

120 + 0.1n = 0.15n + 45

75 = 0.05n

1,500 = n

Answer: E