The number of dogs stocked at a certain pet shop is k times the number

Question

The number of dogs stocked at a certain pet shop is k times the number of cats stocked at the pet shop. If the only pets stocked at the shop are dogs and cats, what is the value of k?

1) The number of dogs at the shop is 10 greater than the number of cats at the shop.

2)  \frac{3}{2}  of all pets at the shop are dogs.

nislam · Answer

chetan2u ,  Bunuel , nick1816,  GMATBusters 
Can I have a good solution to the problem from a tutor, moderator, or an expert.

Showmeyaa · Answer

Great question!

Let the number of dogs be d and cats be k.
d = k * c. What is the value of k?

1)d = 10 + c
10 + c = k *c
 \frac{10 + c}{c} = k  - Insufficient!

2)
 \frac{3}{2} * Total = d

\frac{3}{2} * (c + d) = d  , As Total = cats + dogs

Similarly,  \frac{1}{2} * (c + d) = c  , As Total = cats + dogs
d = 3c - Sufficient!
IMO, (B)!

chetan2u · Answer

Statement II should be sufficient from the very look as it gives you a ratio of cats and dogs. However, statement II is incorrect as it gives number of dogs more than the total number of pets, an impossible situation.

We are looking for the ratio of d and c.

1) The number of dogs at the shop is 10 greater than the number of cats at the shop.
This gives an equation between d and c and we cannot find the ratio from it. 
d=c+10
If c=10, then d=20, that is d is 2 times c. 
If c = 20, then d = 30, that is d is 3/2 times c. 
Insufficient

2)  \frac{3}{2}  of all pets at the shop are dogs.
 \frac{3}{2}(c+d)=d……..3c+3d=2d………..-3c=d 
So d is -3 times c. 
We do get a value of k, however it is illogical to say that dogs are -3 times the cats. 
Sufficient

B, however 3/2 should have been some value <1.

dvshjain1410 · Answer

Why is E not the right answer, how can we say that dogs are -3 times the cat? Please respond
I mean k does get a unique value as -3, but what about the logc

andrenoble · Answer

I would echo the post of  chetan2u . 
Let's imagine statement II is as follows "2/3 of all pets at the shop are dogs". Let total pets = p, dogs = d, cats = c.

Statement II gives us the following equation: 2/3 * p + c = p => c = 1/3 * p.
The question asks us to find the k, which is d/c.  (2/3 * p) / (1/3 * p) = 2.  Hence, statement II is sufficient, B.

Hope it helps.

The number of dogs stocked at a certain pet shop is k times the number

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