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Every student in a room is either a junior or a senior. There is at le

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Every student in a room is either a junior or a senior. There is at le  [#permalink]

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New post 04 Dec 2015, 00:53
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Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 1/4 of the juniors is equal to 3/5 of the seniors, what fraction of the students in the room are juniors?

A. 3/20
B. 1/3
C. 5/12
D. 12/17
E. 17/20

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Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

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New post 04 Dec 2015, 01:51
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Let total number of juniors= J
total number of seniors =S
(1/4) J = (3/5) S
=> S = 5/12 J
Total number of students = J+S = (17/12) J

Fraction of the students in the room are juniors = J/(J+S) = J/[(17/12) J]
=12/17

Answer D
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Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

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New post 06 Dec 2015, 07:26
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Skywalker18 wrote:
Let total number of juniors= J
total number of seniors =S
(1/4) J = (3/5) S
=> S = 5/12 J
Total number of students = J+S = (17/12) J

Fraction of the students in the room are juniors = J/(J+S) = J/[(17/12) J]
=12/17

Answer D


Hi Skywalker18 ,

As soon as we get S = 5/12 J, we can reduce it to ratio of S:J = 5:12.
Now from the above ratio, we can get that number of S and J are 5x and 12x respectively, x being the multiplier.
We can directly calculate J/(J + S) = 12x/17x i.e. 12/17.

So can we say that when we have a relation between two quantities in the form
a/b = int1/int2, we can directly express the fraction of a or b with respect to whole using this relation alone ?

Thanks!
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Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

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New post 06 Dec 2015, 12:10
1
sytabish wrote:
Skywalker18 wrote:
Let total number of juniors= J
total number of seniors =S
(1/4) J = (3/5) S
=> S = 5/12 J
Total number of students = J+S = (17/12) J

Fraction of the students in the room are juniors = J/(J+S) = J/[(17/12) J]
=12/17

Answer D


Hi Skywalker18 ,

As soon as we get S = 5/12 J, we can reduce it to ratio of S:J = 5:12.
Now from the above ratio, we can get that number of S and J are 5x and 12x respectively, x being the multiplier.
We can directly calculate J/(J + S) = 12x/17x i.e. 12/17.

So can we say that when we have a relation between two quantities in the form
a/b = int1/int2, we can directly express the fraction of a or b with respect to whole using this relation alone ?

Thanks!


Hi sytabish ,

Yes , it is essentially the same .

let's say a/b = 1/2
The numbers a and b can be x and 2x respectively , where x is some constant.
a+b= x + 2x = 3x

b/(a+b) =2x/3x = 2/3

a/b + 1 = 1/2 +1
=>(a+b)/b = 3/2
=>b/(a+b) =2/3

a/(a+b)=x/3x = 1/3

or b/a = 2
=>b/a + 1 = 2+1
=>(b+a)/a = 3
=>a/(a+b)=1/3

Hope it help!! :)
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Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

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New post 06 Dec 2015, 12:26
Bunuel wrote:
If 1/4 of the juniors is equal to 3/5 of the seniors, what fraction of the students in the room are juniors?/


\(\frac{1}{4}J\) = \(\frac{3}{5}S\)

So, J = \(\frac{12}{5}s\)

Bunuel wrote:
Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room.


So, Total no of Students in the room is = junior + senior

Or, Total no of Students in the room is = \(\frac{12}{5}s\)+ \(s\)

Or, Total no of Students in the room is = \(\frac{17}{5}s\)

Bunuel wrote:
What fraction of the students in the room are juniors?


Required Fraction is = Juniors/Total Number of Students

Or, Required Fraction is =12s/5/17s/5

Or, The Required Fraction is = 12/17


Hence answer is (D) 12/17

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Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

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New post 07 Dec 2015, 22:29
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Hi All,

This question can be solved by TESTing VALUES. The 'key' is to make sure that the NUMERATORS of the two fractions are equal.

We're told that 1/4 of the Juniors = 3/5 of the Seniors

With these two fractions, the easiest way to set the two numbers equal is if we use the number 3...

3 out of 12 Juniors = 3 out of 5 Seniors

So there are 12 TOTAL Juniors and 5 TOTAL Seniors

The question asks what fraction of the students are JUNIORS: 12/17

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Re: Every student in a room is either a junior or a senior. There is at le  [#permalink]

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New post 28 Oct 2016, 17:07
Say # of juniors = 120

1/4(120)=(3/5)x
30=3x/5
x=50 (# seniors)

120+50 = 170 (total of people in the room)

ratio --> 120/170 = 12/17
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