Of the birds in a particular aviary, 30 are both spotted and

First tabulate the data which is provided to us in the question stem

To find: Total number of birds in the aviary

Let Not spotted and Crested be y

1) we are just given the relationship between NS, C and NC, S

NC,S = y +10, Cant tell anything from here

(2) More than 3/5 of the birds in the aviary are spotted.

Now this can be any value, again we dont know the fix value of the total number of birds

--------S--------NS-----
C------30--------y----- 30+y
NC----y+10-----10---- y +20
------y+40------10y----x

Now even if i make 2 equations after combining

50 +2y = 50y +40
10 /48 = y

It can be any value, since i dont know what is the value coming after 3/5 of the birds are spotted

E

Hi VeritasKarishma

Just wondering in such DS questions, is it necessary to figure out the math? Because we can use logic to eliminate and arrive at the answer. Or is that a risky approach? As in some questions we may find a new constraint or arrive at the something concrete which might potentially remain hidden if we don't work out the math and make some equations/inequalities. We can either solve the question quick by using logic , save time and risk missing something or we can approach it in a more elaborate way which would guarantee a correct answer but on the expense of more time. How to make this decision ?

We do not need to solve DS questions but we need to be certain of the answer (as per our capability). If use of logic clarifies the statement(s) that are sufficient/insufficient, great! If you are not sure, it is best to work out at least partially. Cases in which there are some unwritten constraints like this question (no. of birds will be an integer), it is advisable to work out the math a little bit. The statements alone do not require much work. But when I think the answer is (E), I like to figure out two distinct possible values that satisfy all constraints. Only then do I mark it as (E).

I see the values you got for 30+y, y+20 and y+40 were all added together but why did you multiply to get 10y? Shouldn't this be y+10?

Official Explanation:

The information presented can be set up in a Double-Set Matrix:

C No C Total
S 30
No S 10
Total ?
(1) INSUFFICIENT: If x represents the number of birds that are crested but not spotted, this statement yields the following:

C No C Total
S 30 x + 10 x + 40
No S x 10 x + 10
Total x + 30 x + 20 2x + 50 = ?
Without a value for x, it is not possible to find the total.

(2) INSUFFICIENT: By itself, this statement does not provide values for any unknowns in the problem.

C No C Total
S 30 > 3/5 Total
No S 10 < 2/5 Total
Total Total = ?

(1) and (2) INSUFFICIENT: The two statements together provide a filled-in matrix and a relationship between the total number of spotted birds and the total number of birds in the aviary. However, this only provides a range for the total:

C No C Total
S 30 x + 10 x + 40
No S x 10 x + 10
Total x + 30 x + 20 2x + 50 = ?
Total S > 3/5 of Total Birds
x + 40 > 3/5 (2x + 50)
x + 40 > 6x/5 + 30
10 > x/5
50 > x

If x < 50, the total number of birds, 2x + 50, must be less than 150, but this does not provide a definitive value for the total.

The correct answer is (E).