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# In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4487
In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up  [#permalink]

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20 Oct 2014, 11:50
00:00

Difficulty:

35% (medium)

Question Stats:

77% (02:46) correct 23% (02:55) wrong based on 151 sessions

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In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Upperclassmen, drawn from three cities: A, B, and C. Sixty percent of students are from A, 30% from B, the rest from C, and all these students from C are freshmen. Half the student from B are upperclassman, and the rest are split evenly between the other two grades. How many sophomores are from A?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100

For a discussion of the Double Matrix method for solving questions of this sort, as well as the OE for this question, see:
https://magoosh.com/gmat/2014/gmat-prac ... lems-sets/

Mike

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Mike McGarry
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In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up  [#permalink]

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20 Oct 2014, 21:09
3

Solved using matrix method as below:

Attachment:

mat.png [ 6.72 KiB | Viewed 2455 times ]

1. Total Freshmen = 80

2. Total Sophomores = 100

3. Total Upperclassmen = 220

4. Net people = 80+100+220 = 400

5. 60% from A $$= \frac{60}{100} * 400 = 240$$

6. 30% from B $$= \frac{30}{100} * 400 = 120$$

7. Remaining from C = 400 - (240+120) = 40

8. All students of C are Freshmen = 40

9. Half the student from B are upperclassman = 120/2 = 60

10. rest are split evenly between the other two grades = 30

11. rest are split evenly between the other two grades = 30

12. How many sophomores are from A = 100 - 30 = 70
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Re: In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up  [#permalink]

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22 Jan 2015, 23:46
1
Ans B = 70

I don't know how to upload the sceenshot but I used 3*3 Matrix

F S U Total
A ? 240
B 30 30 60 120
C 40 0 0 40

Total 80 100 220 400

On solving we get ? = 70
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Re: In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up  [#permalink]

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23 Jan 2015, 02:30
1
This is a repeated question... have solved it detailed below

in-a-certain-school-there-are-80-freshmen-100-sophomores-and-220-up-187208.html?fl=similar
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Re: In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up  [#permalink]

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27 Feb 2017, 04:31
the answer should be B we can solve it by suing matrix method .
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Re: In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up  [#permalink]

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18 Aug 2018, 09:22
Attachments

ABC.png [ 30.38 KiB | Viewed 508 times ]

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Joined: 17 Aug 2018
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Re: In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up  [#permalink]

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18 Aug 2018, 10:29
First step is calculating total no. of students which is 400 and then neglecting C for the calculation as it contains only Frshman. Out of A and B we can quickly cal total no. of B which is 0.30 * 400 = 120 and then out of which half is upperman I.e. 60 remaining half is 60 which is divided into 30 and 30

So out of total 100 shopomores 30 are from B so rest are from A i.e. 70

Posted from my mobile device
Re: In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Up   [#permalink] 18 Aug 2018, 10:29
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