GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 09:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# There are 300 seniors at Morse High School, and 40% of them have cars.

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58465
There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

06 Mar 2015, 07:40
3
1
00:00

Difficulty:

35% (medium)

Question Stats:

81% (02:33) correct 19% (02:22) wrong based on 108 sessions

### HideShow timer Statistics

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

Kudos for a correct solution.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8023
Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

06 Mar 2015, 18:18
Bunuel 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

Kudos for a correct solution.

as 40% of 300 seniors have car, the number=120...
let the remaining grades be x...
10% of x=.1x...
combined=120+.1x, now it is given that this is equal to .15(x+300)..
120+.1x=.15(x+300)...
x=1500
ans E
_________________
Manager
Joined: 04 Jun 2013
Posts: 61
Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

07 Mar 2015, 00:02
1
I think the ans should be (E).
Let the total no of students be n.
The no of seniors having cars is 40% of 300 i.e. 120.
The rest of the students with other three grades who have cars is 10% of (n-300).
The total no of students with cars is 15% of n.
Thus, 0.15n= 120+0.1(n-300)
On solving this, we get n=1800.
Hence, the no of students with other three grades is 1800-300, i.e. 1500 (E).
Director
Joined: 21 May 2013
Posts: 635
Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

07 Mar 2015, 00:08
1
Bunuel 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

Kudos for a correct solution.

+1 for E .15X+45=120+.1X
X=1500
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15315
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

07 Mar 2015, 00:22
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.

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"

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.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

07 Mar 2015, 03:13
Using a table to organise all the information we get this:
S = Sophomore and NS = Not Sophomore
Yes = Yes car and No = No car

.................Yes.................No.........All
S...............120.................280........300
NS............0.10x................................
All.........0.15(x+300)............................

So:
120 + 0.10x = 0.15(x+300)
120 + 0.10x = 0.15x + 45
75 = 0.05x
x = 1500 ANS E
Math Expert
Joined: 02 Sep 2009
Posts: 58465
Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

08 Mar 2015, 15:17
Bunuel 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

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Let x = the number of students other than seniors (freshmen + sophomores + junior). We know 40% of the 300 seniors have cars. Well, 10% of 300 is 30, so 40% is 4 times this —- 4*30 = 120 seniors have cars. We know 10% of the other students have cars, so that would be 0.1*x. The total number of students with cars is 120 + 0.1x. That’s the PART.

The total number of students = 300 + x. That’s the WHOLE.

PART/ WHOLE x 100% = 15%, which means that PART/ WHOLE = 0.15, which means PART = 0.15*(WHOLE). That can be our equation.
(120 + 0.1x) = 0.15(300 + x)
120 + 0.1x = 45 + 0.15x
75 + 0.1x = 0.15x
75 = 0.15x – 0.10x = 0.05x
150 = 0.10x
1500 = x

_________________
Intern
Joined: 11 Dec 2016
Posts: 47
Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

20 Feb 2019, 04:59
Hi, can this be solved by using the weighted averages concept? VeritasKarishma
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

20 Feb 2019, 10:08
1
asfandabid wrote:
Hi, can this be solved by using the weighted averages concept? VeritasKarishma

Yes, absolutely!

Average of 10% and 40% is 15%,

wO/wS = (40 - 15)/(15 - 10) = 5/1

Ratio of number of students in other grades : Seniors = 5 : 1
Since there are 300 seniors, students in other grades = 1500

_________________
Karishma
Veritas Prep GMAT Instructor

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8137
Location: United States (CA)
Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

### Show Tags

22 Feb 2019, 16:38
Bunuel 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

Kudos for a correct solution.

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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: There are 300 seniors at Morse High School, and 40% of them have cars.   [#permalink] 22 Feb 2019, 16:38
Display posts from previous: Sort by