Cat & Owners

[sandipgumtya]

In a group of cats and their owners, how
many cats are there?
(1) There are 84 legs in total in the group.
(2) The difference between the number of
cats and their owners is 6.

I cant find reasons to agree with OA-C

[theCEO]

In a group of cats and their owners, how
many cats are there?
(1) There are 84 legs in total in the group.
(2) The difference between the number of
cats and their owners is 6.

I cant find reasons to agree with OA-C

1) Insufficient on its own.
C = number of cats
o = number of owners
4C + 2o = 84

2) Insufficient on its own
C - o = 6
C = 6 + o

Combining both equation:

The difference between the number of cats and their owners is
C - o = 6
C = 6 + o
o = C - 6

legs from cats = 4 x number of cats = 4C = 4(6+o) = 24 + 4o
legs from owner= 2 x number of owners = 2o = 2(C-6) = 2C - 12

Total legs = 24 + 4o + 2C - 12 = 84
12 + 4o + 2(6+o) = 84
12 + 4o + 12 + 2o = 84
24 + 6o = 84
6o = 60
o = 10

If owner = 10
cats = 10 + 6 = 16

Suffincent. Ans = C

[Ian Stewart]

I gather we're meant to assume that cats all have 4 legs, and owners all have 2 legs. Then if we have c cats, and ø owners, Statement 1 tells us that

4c + 2ø = 84

which has a lot of possible positive integer solutions, and Statement 2 tells us that

c - ø = 6

which also has a lot of possible positive integer solutions. Taking the two statements together, we have two different linear equations in two unknowns, so we can solve. It's a DS question, so there's no need to actually solve, but if we wanted an answer, we could use substitution, or multiply the second equation by 2 and add the two equations:

4c + 2ø = 84
2c - 2ø = 12
6c = 96
c = 16

At first glance, I thought the meaning of Statement 2 was ambiguous, because it talks about a difference, but doesn't tell us which quantity is larger - it could mean either:

c - ø = 6

or

ø - c = 6

But the question is about owners of cats, and we can't have more owners than cats, because each owner must own at least 1 cat just to be a cat-owner at all. So the equation needs to be the one I used in the solution above, and cannot be ø - c = 6.

[sandipgumtya]

I am getting following two cases:

Case 1:Owner-10 and Cat-16
Case 2: Owner-18 and Cat-12.

Both satisfy all the conditions.How can we uniquely determine no of Cats.?

[theCEO]

I am getting following two cases:

Case 1:Owner-10 and Cat-16
Case 2: Owner-18 and Cat-12.

Both satisfy all the conditions.How can we uniquely determine no of Cats.?

you cannot have more owners than cats.
in other words, you cannot have more cat owners than cats.