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

Question

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

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

Zarrolou · Accepted Answer

\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}

Carcass · Answer

Correct

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elisabettaportioli · Answer

Zarrolou

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

Thanks in advance!

Lucky2783 · Answer

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

Answer C

EMPOWERgmatRichC · Answer

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

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

Dokami · Answer

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

generis · Answer

ratiotable.png 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? Dump Sociology now. You're not being asked about it. 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 Answer C Hope that helps.

Dokami · Answer

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

nkmungila · Answer

Answer C

3/4*3/5*2/5

bumpbot · Answer

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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

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