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

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

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New post 06 Mar 2015, 07:40
3
1
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

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

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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



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Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

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New post 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
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Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

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New post 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).
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Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

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New post 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
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Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

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New post 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.

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:

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

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New post 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
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Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

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New post 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

Answer = (E)
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Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

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New post 20 Feb 2019, 04:59
Hi, can this be solved by using the weighted averages concept? VeritasKarishma
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Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

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New post 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

Answer (E)
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Re: There are 300 seniors at Morse High School, and 40% of them have cars.  [#permalink]

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New post 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

Answer: E
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Re: There are 300 seniors at Morse High School, and 40% of them have cars.   [#permalink] 22 Feb 2019, 16:38
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