The ratio of spinsters to cats is 2 to 7. If there are 25

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Jul 22, 2018 2:39 am

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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

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Source: Beat The GMAT — Problem Solving | Sun Jul 22, 2018 2:39 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 22, 2018 3:24 am

BTGmoderatorDC 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

Given ratio = S:C = 2:7.
The difference between the parts of the ratio = 7-2 = 5.
Since the actual difference between the number of cats and the number of spinsters is five times as great -- 25 -- each part of the ratio must be multiplied by a FACTOR OF 5:
S:C = (2*5) : (7*5) = 10:35, with the result that there are 25 more cats than spinsters.
Thus, S=10.

The correct answer is A.

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by [email protected] » Sun Jul 22, 2018 9:09 am

Hi All,

We're told that the ratio of spinsters to cats is 2 to 7 and that there are 25 MORE cats than spinsters. We're asked for the number of spinsters. This question can be solved in a number of different ways, including by TESTing THE ANSWERS. Let's TEST Answer B first.

Answer B: 12
IF... there are 12 spinsters, then there are 6 'groups' of 2 spinsters, so...
there will be 6 'groups' of 7 cats, giving us 6(7) = 42 cats
Here, the difference between the number of cats and the number of spinsters is 42 - 12 = 30. This is TOO HIGH (the difference is supposed to be 25). Increasing the number of spinsters would INCREASE the difference, so we have to look for a SMALLER answer. There's only one answer left....

If you wanted to prove that the correct answer was Answer A, the work would be the same as above...
IF... there are 10 spinsters, then there are 5 'groups' of 2 spinsters, so...
there will be 5 'groups' of 7 cats, giving us 5(7) = 35 cats
Here, the difference between the number of cats and the number of spinsters is 35 - 10 = 25. This is an exact match for what we were told, so this must be the answer.

Final Answer: A

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Mon Jul 23, 2018 11:17 am

BTGmoderatorDC 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

What is the source of this question?! The real GMAT would never use a term as misogynistic as "spinster."

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Wed Jul 25, 2018 4:31 pm

BTGmoderatorDC 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

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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Head of GMAT Instruction
[email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 09, 2020 6:03 am

BTGmoderatorDC 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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