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# At a certain school, the ratio of the number of English

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At a certain school, the ratio of the number of English [#permalink]

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30 Mar 2013, 09:49
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At a certain school, the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4. If the ratio of the number of History majors to the number of English majors is 5 to 3, what is the ratio of the number of Psychology majors to the number of History majors?

(A) 25 to 3
(B) 10 to 9
(C) 9 to 50
(D) 6 to 25
(E) 3 to 10
[Reveal] Spoiler: OA

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Re: At a certain school, the ratio of the num [#permalink]

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30 Mar 2013, 09:57
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$$\frac{E}{S} = \frac{5}{2}, \frac{P}{S}=\frac{3}{4}, \frac{H}{E}=\frac{5}{3}$$

$$\frac{P}{H}=?$$

$$\frac{P}{H}=\frac{P}{S}*\frac{S}{E}*\frac{E}{H}$$

$$\frac{P}{H}=\frac{3}{4}*\frac{2}{5}*\frac{3}{5}$$

$$\frac{P}{H}=\frac{9}{50}$$
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Re: R: At a certain school, the ratio of the number of English [#permalink]

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31 Mar 2013, 06:36
Correct

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Re: At a certain school, the ratio of the number of English [#permalink]

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01 Apr 2015, 03:28
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Zarrolou wrote:
$$\frac{E}{S} = \frac{5}{2}, \frac{P}{S}=\frac{3}{4}, \frac{H}{E}=\frac{5}{3}$$

$$\frac{P}{H}=?$$

$$\frac{P}{H}=\frac{P}{S}*\frac{S}{E}*\frac{E}{H}$$

$$\frac{P}{H}=\frac{3}{4}*\frac{2}{5}*\frac{3}{5}$$

$$\frac{P}{H}=\frac{9}{50}$$

Zarrolou

Can you explain by which rule/reasoning did you multiply the following?
P/H=P/S*S/E*E/H

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Re: At a certain school, the ratio of the number of English [#permalink]

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01 Apr 2015, 03:41
carcass wrote:
At a certain school, the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4. If the ratio of the number of History majors to the number of English majors is 5 to 3, what is the ratio of the number of Psychology majors to the number of History majors?

(A) 25 to 3
(B) 10 to 9
(C) 9 to 50
(D) 6 to 25
(E) 3 to 10

$$\frac{P}{S} * \frac{E}{H}* \frac{S}{E} = \frac{3}{4} * \frac{3}{5} *\frac{2}{5}$$

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Re: At a certain school, the ratio of the number of English [#permalink]

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02 Apr 2015, 22:31
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Hi All,

This series of 'overlapping' ratios can be dealt with by TESTing VALUES.

We're given the following ratios to work with:

E:S
5:2

P:S
3:4

H:E
5:3

We're asked for the ratio of P:H

Based on the given ratios, we know that E is a multiple of BOTH 3 and 5, so let's TEST E = 15....

IF....
E = 15
Then.....
S = 6
P = 4.5
H = 25

We now have a "grand ratio" that involves all 4 variables. Since we cannot have "half" a Psychology teacher, we can multiply each of these values by 2....this gives us....

E = 30
S = 12
P = 9
H = 50

The question asks for the ratio of the number of Psychology majors to the number of History majors...

P:H
9:50

[Reveal] Spoiler:
C

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Re: At a certain school, the ratio of the number of English [#permalink]

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03 Nov 2017, 07:11
Please, do anybody know how to solve the problem with a ratio box?

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At a certain school, the ratio of the number of English [#permalink]

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03 Nov 2017, 11:20
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Quote:
carcass wrote
At a certain school, the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4. If the ratio of the number of History majors to the number of English majors is 5 to 3, what is the ratio of the number of Psychology majors to the number of History majors?

(A) 25 to 3
(B) 10 to 9
(C) 9 to 50
(D) 6 to 25
(E) 3 to 10

Dokami wrote:
Please, do anybody know how to solve the problem with a ratio box?

Attachment:

ratiotable.png [ 17.87 KiB | Viewed 353 times ]

Dokami , I used one. It's quick; a little over a minute

Take it in two stages. Each discipline is represented by its first letter (English = E, etc.)

1) the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4.

E:S = 5:2 and P:S = 3:4 (watch order here -- you need to switch the latter in the table, Box A)
Sociology is the common term. Put it in the middle.

Box A: has split ratios because common term S has different values in each ratio:
E: S = 5:2, and S:P = 4:3

Box B: the result of multiplying the TOP ROW ONLY by 2 (so that S can = 4 in both ratios)

Box C: Combine into one row. . . .E: S: P = 10: 4: 3

2) The ratio of the number of History majors to the number of English majors is 5 to 3. What is the ratio of the number of Psychology majors to the number of History majors?

H:E=5:3 and what is P:H?

Bring the numbers for (E:P) down from Box C to Box D

Box D: The common term is E. It goes in the middle.
Split the ratios again because E is not the same.

H:E = 5:3, and E:P = 10:3

This time, to get E to have the same value, LCM of 3 and 10 is 30.
Multiply top row by 10, bottom row by 3.

Box E: the result of multiplying each row by a different factor, so E now = 30

Box F: combined results
H: E: P
50:30:9

Ratio of number of P to H? From Box F
9:50

Hope that helps.

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Re: At a certain school, the ratio of the number of English [#permalink]

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03 Nov 2017, 11:55
Thank you very much genxer 123!
I also found a solution. My handwriting is not the best, but I hope you can follow me anyway
Attachments

aaaa.jpg [ 3.55 MiB | Viewed 331 times ]

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Re: At a certain school, the ratio of the number of English [#permalink]

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04 Nov 2017, 02:00

3/4*3/5*2/5
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Re: At a certain school, the ratio of the number of English   [#permalink] 04 Nov 2017, 02:00
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