Data Sufficiency

Carol has three different kinds of pets dogs, cats and rabbits. The number of pets of each kind with
Carol is more than 1 but is not more than 6. If the total number of pets with Carol is 12, then what is the
number of rabbits with Carol?


A: The number of dogs is same as the number of cats and the number of rabbits is not more than the
number of dogs.
B: The number of cats is three more than the number of dogs and the number of rabbits is less than the
number of cats.

harsh.champ wrote:Carol has three different kinds of pets dogs, cats and rabbits. The number of pets of each kind with
Carol is more than 1 but is not more than 6. If the total number of pets with Carol is 12, then what is the
number of rabbits with Carol?


A: The number of dogs is same as the number of cats and the number of rabbits is not more than the
number of dogs.
B: The number of cats is three more than the number of dogs and the number of rabbits is less than the
number of cats.

A insufficient
B. insufficient

combined contradictory
A says D=C
B says C= 3+D

[spoiler]
ans is E[/spoiler]

What is OA?

I get that both statements by themselves are sufficient, but combined are contradictory.

Constraints; (Both 1&2) D+C+R=12; D,C,R>1 ; D,C,R <=6

1) D=C, R>D
Therefore 12=R+2C,
(a) If R=6, D=3, C=3; fits all constraints
(b) If R=5, D=3.5, C=3.5; cannot have half a dog and half a cat; not logical
(c) If R=4, D=4, C=4, but R is no longer >D, therefore does not fit with constraints
(d) If R=8, D=2, C=2, but R is no longer <=6, therefore does not fit with constraints
(e) R<=3 has same problem as b, R>=7 has same problem as d; therefore A is the only possible solution, R must equal 6, SUFFICIENT

2) C=D+3, R<C
(a) If C=6, D=3, R=3, fits all constraints
(b) If C=5, D=2, R=5; R no longer <C, therefore does not fit with constraints
(c) C=(1-4) will not fit constraint as per (b)
(d)C=(>7) will not fit initial constraint, as D,C,R must be <=6. Therefore, R must equal 3. SUFFICIENT

1 & 2 are contradictory, however. Did I mess up somewhwere?

BSDesis wrote:What is OA?

I get that both statements by themselves are sufficient, but combined are contradictory.

Constraints; (Both 1&2) D+C+R=12; D,C,R>1 ; D,C,R <=6

1) D=C, R>D
Therefore 12=R+2C,
(a) If R=6, D=3, C=3; fits all constraints
(b) If R=5, D=3.5, C=3.5; cannot have half a dog and half a cat; not logical
(c) If R=4, D=4, C=4, but R is no longer >D, therefore does not fit with constraints
(d) If R=8, D=2, C=2, but R is no longer <=6, therefore does not fit with constraints
(e) R<=3 has same problem as b, R>=7 has same problem as d; therefore A is the only possible solution, R must equal 6, SUFFICIENT

2) C=D+3, R<C
(a) If C=6, D=3, R=3, fits all constraints
(b) If C=5, D=2, R=5; R no longer <C, therefore does not fit with constraints
(c) C=(1-4) will not fit constraint as per (b)
(d)C=(>7) will not fit initial constraint, as D,C,R must be <=6. Therefore, R must equal 3. SUFFICIENT

1 & 2 are contradictory, however. Did I mess up somewhwere?

Hey BSDesis,
The OA is B.
Let me denote the pets as C,D and R.
For statement A,
The number of C and D with Carol could be (3, 3) or (4, 4) or (5, 5).
The number of R when the number of D is 5, 3 and 4 is 2, 6 and 4 respectively.
It is also given that the number of R is not more than the number of D, so the number of R could be either 2 or 4.
Hence, statement A is insufficient.

I hope it is clear now why statement A is insufficient.

harsh.champ wrote:
Hey BSDesis,
The OA is B.
Let me denote the pets as C,D and R.
For statement A,
The number of C and D with Carol could be (3, 3) or (4, 4) or (5, 5).
The number of R when the number of D is 5, 3 and 4 is 2, 6 and 4 respectively.
It is also given that the number of R is not more than the number of D, so the number of R could be either 2 or 4.
Hence, statement A is insufficient.

I hope it is clear now why statement A is insufficient.

Harsh you say that OA is B, You have givena a good explanation for insufficiency of A .. But how do you explain the sufficiency of B..

Sure.
I am using the same nomenclature as before (C,D and R)

Using Statement B:
The number of C and D with Carol could be (5, 2) or (6, 3) in this particular order.
The number of R with Carol when there are 5 C is 5 and the number of rabbits with Carol when there are 6 C is 3.
Now we know that the R < C. therefore the number of rabbits with Carol is 3.
Hence, statement B alone is sufficient to answer the question.

For approach involving inequalities you can refer to the post made by BSDesis below:-

2) C=D+3, R<C
(a) If C=6, D=3, R=3, fits all constraints
(b) If C=5, D=2, R=5; R no longer <C, therefore does not fit with constraints
(c) C=(1-4) will not fit constraint as per (b)
(d)C=(>7) will not fit initial constraint, as D,C,R must be <=6. Therefore, R must equal 3. SUFFICIENT

harsh.champ wrote:Sure.
I am using the same nomenclature as before (C,D and R)

Using Statement B:
The number of C and D with Carol could be (5, 2) or (6, 3) in this particular order.
The number of R with Carol when there are 5 C is 5 and the number of rabbits with Carol when there are 6 C is 3.
Now we know that the R < C. therefore the number of rabbits with Carol is 3.
Hence, statement B alone is sufficient to answer the question.

For approach involving inequalities you can refer to the post made by BSDesis below:-

2) C=D+3, R<C
(a) If C=6, D=3, R=3, fits all constraints
(b) If C=5, D=2, R=5; R no longer <C, therefore does not fit with constraints
(c) C=(1-4) will not fit constraint as per (b)
(d)C=(>7) will not fit initial constraint, as D,C,R must be <=6. Therefore, R must equal 3. SUFFICIENT

Ok I got ur answer .. thanks for the same...

Why are the two statements contradicting each other?

As far as I know the the statements should never contradict each other in the GMAT question

1) says that the number of cats and dogs is equal and 2) says that the cats are three more than the dogs

Could you please tell is the source of this Question?

hd1 wrote:Why are the two statements contradicting each other?

As far as I know the the statements should never contradict each other in the GMAT question

1) says that the number of cats and dogs is equal and 2) says that the cats are three more than the dogs

Could you please tell is the source of this Question?

Valid point cos, Option C cannot exist otherwise.