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Fraction/Ratio

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Fraction/Ratio

by BTGmoderatorRO » Fri Dec 29, 2017 4:59 am

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Local kennel has cats and dogs in the ratio of 5:6. If there are 18 fewer cats than dogs, how many dogs are in the kennel?

A. 60
B. 74
C. 98
D. 108
E. 132

OA is D

OA says D but I solved and got E can an Expert shoe some solutions? Thanks
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Fraction/Ratio

by EconomistGMATTutor » Fri Dec 29, 2017 11:28 am
Local kennel has cats and dogs in the ratio of 5:6. If there are 18 fewer cats than dogs, how many dogs are in the kennel?

A. 60
B. 74
C. 98
D. 108
E. 132

OA is D

OA says D but I solved and got E can an Expert shoe some solutions? Thanks
Hi Roland2rule,
Let's take a look at your question.

If C denotes cats and D denotes dogs, then,
$$\frac{C}{D}=\frac{5}{6}$$
$$6C=5D...(i)$$

If there are 18 fewer cats then dogs, we can write it as,
$$C=D-18$$

Substitute C in eq(i),
$$6\left(D-18\right)=5D$$
$$6D-108=5D$$
$$6D-5D=108$$
$$D=108$$

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
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by Scott@TargetTestPrep » Sun Aug 25, 2019 5:48 pm
BTGmoderatorRO wrote:Local kennel has cats and dogs in the ratio of 5:6. If there are 18 fewer cats than dogs, how many dogs are in the kennel?

A. 60
B. 74
C. 98
D. 108
E. 132

OA is D

OA says D but I solved and got E can an Expert shoe some solutions? Thanks
We can express the ratio of cats to dogs as 5x : 6x. We can create the equation:

6x - 5x = 18

x = 18

Thus, there are 6 x 18 =108 dogs in the kennel.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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by Brent@GMATPrepNow » Mon Aug 26, 2019 4:56 am
BTGmoderatorRO wrote:Local kennel has cats and dogs in the ratio of 5:6. If there are 18 fewer cats than dogs, how many dogs are in the kennel?

A. 60
B. 74
C. 98
D. 108
E. 132
Let D = # of Dogs
Let C = # of Cats

There are 18 fewer cats than dogs.
So, C = D - 18

cats and dogs are in the ratio of 5:6
We get: C/D = 5/6
Cross multiply to get: 6C =5D

Take 6C =5D and replace C with D - 18 to get: 6(D - 18) = 5D
Expand: 6D - 108 = 5D
Subtract 6D from both sides to get: -108 = -D
So, D = 108

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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