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# At a certain college, the ratio of students to professors is

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At a certain college, the ratio of students to professors is [#permalink]  19 Aug 2018, 03:03
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Question Stats:

77% (01:04) correct 22% (01:01) wrong based on 18 sessions
At a certain college, the ratio of students to professors is 8 : 1 and the ratio of students to administrators is 5 : 2. No person is in more than one category (for instance, there are no administrators who are also students).

 Quantity A Quantity B The fractional ratio of professors to administrators $$\frac{5}{8}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: At a certain college, the ratio of students to professors is [#permalink]  20 Aug 2018, 07:33
Expert's post
sandy wrote:
At a certain college, the ratio of students to professors is 8 : 1 and the ratio of students to administrators is 5 : 2. No person is in more than one category (for instance, there are no administrators who are also students).

 Quantity A Quantity B The fractional ratio of professors to administrators $$\frac{5}{8}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Notice that the number of students is common to BOTH ratios

Ratio of students to professors is 8 : 1
So, S : P = 8 : 1

Ratio of students to administrators is 5 : 2
So, S : A = 5 : 2

In order to COMBINE the two ratios, we must find EQUIVALENT ratios such that we have the same number of students in each ratio.

Take: 8 : 1 and multiply both sides by 5 to get the EQUIVALENT ratio: S : P = 40 : 5
Next, take: 5 : 2 and multiply both sides by 8 to get the EQUIVALENT ratio: S : A = 40 : 16

We can now COMBINE the two ratios to get: S : P : A = 40 : 5 : 16

We have:
Quantity A: P/A (aka P : A)
Quantity B: 5/8

From our ratio S : P : A = 40 : 5 : 16, we can see that P/A = 5/16

So, we have:
Quantity A: 5/16
Quantity B: 5/8

So, Quantity B is greater.

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Re: At a certain college, the ratio of students to professors is   [#permalink] 20 Aug 2018, 07:33
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