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Fraction/Ratio

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Fraction/Ratio

by BTGmoderatorRO » Fri Dec 29, 2017 5:12 am
The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?

A. 10
B. 12
C. 15
D. 18
E. 27

OA is A

What is the best approach to solving this question?
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Fraction/Ratio

by EconomistGMATTutor » Fri Dec 29, 2017 11:16 am
The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?

A. 10
B. 12
C. 15
D. 18
E. 27

OA is A

What is the best approach to solving this question?
Hi Roland2rule,
Let's take a look at your question.

Let S denotes the spinsters and C denotes the cats, then
$$\frac{S}{C}=\frac{2}{7}$$
$$7S=2C ... (i)$$

If there are 25 more cats then spinsters, we can write it as,
$$C=S+25$$
Substitute C in eq(i), we get,
$$7S=2\left(S+25\right)$$
$$7S=2S+50$$
$$7S-2S=50$$
$$5S=50$$
$$S=\frac{50}{5}=10$$
When there are 25 more cats then spinsters, then there are 10 spinsters.

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.
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by Brent@GMATPrepNow » Fri Dec 29, 2017 12:44 pm
Roland2rule wrote:The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?

A. 10
B. 12
C. 15
D. 18
E. 27
Another option is to list equivalent ratios

GIVEN: The ratio of spinsters to cats is 2 to 7
So, it's possible that there are 2 spinsters and 7 cats [difference = 7 - 2 = 5.....we need a difference of 5]
It's also possible that there are 4 spinsters and 14 cats [difference = 14 - 4 = 10.....we need a difference of 5]
Or there are 6 spinsters and 21 cats [difference = 15.....we need a difference of 5]
Or there are 8 spinsters and 28 cats [difference = 20.....we need a difference of 5]
Or there are 10 spinsters and 35 cats [difference = 25.... BINGO!!!]

So, there are 10 spinsters
Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Sun Aug 25, 2019 5:48 pm
BTGmoderatorRO wrote:The ratio of spinsters to cats is 2 to 7. If there are 25 more cats than spinsters, how many spinsters are there?

A. 10
B. 12
C. 15
D. 18
E. 27

OA is A

What is the best approach to solving this question?
We can re-express the ratio of spinsters to cats as 2x : 7x, where 2x = the number of spinsters and 7x = the number of cats. We can create the equation:

7x - 25 = 2x

5x = 25

x = 5

Thus, there are 2 * 5 = 10 spinsters.

Answer: A

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