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There are 240 doctors and nurses at a hospital. If the ratio

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by VJesus12 » Sat Nov 23, 2019 2:37 am
There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180

[spoiler]OA=D[/spoiler]

Source: Princeton Review
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by Brent@GMATPrepNow » Sat Nov 23, 2019 7:52 am
VJesus12 wrote:There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180

[spoiler]OA=D[/spoiler]

Source: Princeton Review

The ratio of doctors to nurses is 5 to 7
5 + 7 = 12.
So we can say that, for every 12 workers, 5 are doctors and 7 are nurses.
In other words, 7/12 of the workers are nurses.

We are told that there are 240 workers in total
So, the total number of nurses = 7/12 of 240
= (7/12)(240)
= 140

Answer: D

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by Brent@GMATPrepNow » Sat Nov 23, 2019 8:32 am
VJesus12 wrote:There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180
Here's a different approach:

If the ratio of doctors to nurses is 5 to 7, then some possible scenarios are:
- 5 doctors and 7 nurses.
- 10 doctors and 14 nurses.
- 15 doctors and 21 nurses.
- 20 doctors and 28 nurses.
etc
As we can see, the total number of nurses is always divisible by 7
When we check the answer choices, only answer choice D is divisible by 7

Answer: D

Cheers,
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by [email protected] » Sat Nov 23, 2019 9:47 am
Hi VJesus12,

We're told that there are 240 doctors and nurses at a hospital and the ratio of doctors to nurses is 5 to 7. We're asked for the number of NURSES at the hospital. This question can be solved in a variety of different ways, including by TESTing THE ANSWERS.

Since the ratio of doctors to nurses is 5:7, the ratio of nurses to ALL people is 7:(5+7) = 7:12. Thus, the correct answer - when divided by 240 - will equal 7/12.

With a ratio of 5:7, MORE than half of the people are nurses, so we should start with an answer that is greater than half of 240. Let's TEST Answer D first...

Answer D: 140
IF.... there are 140 nurses, then the ratio of nurses:all = 140:240 = 140/240 = 14/24 = 7/12.
This is an exact match for what we are looking for, so this must be the answer.

Final Answer: D

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by Scott@TargetTestPrep » Fri Dec 13, 2019 1:08 pm
VJesus12 wrote:There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180

[spoiler]OA=D[/spoiler]

Source: Princeton Review
We can create the equation:

240 = 5x + 7x

240 = 12x

20 = x

So there are 7 * 20 = 140 nurses.

Answer: D

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