j_shreyans wrote:Of the birds in a particular aviary, 30 are both spotted and crested and 10 are neither spotted nor crested. What is the total number of birds in the aviary?
(1) The number of birds that are spotted but not crested is 10 greater than the number of birds that are crested but not spotted.
(2) More than 3/5 of the birds in the aviary are spotted.
This is an EITHER/OR group problem.
Every bird is EITHER spotted OR not.
Every bird is EITHER crested OR not.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.
Let S = spotted, NS = not spotted, C = crested, NC = not crested.
In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.
Prompt:
30 are both spotted and crested and 10 are neither spotted nor crested.
What is the total number of birds in the aviary?
The following grid is yielded:
We need the value represented by the question mark.
Statement 1: The number of birds that are spotted but not crested is 10 greater than the number of birds that are crested but not spotted.
The following grid is yielded:
In the resulting grid, the total number of birds = 2x+50.
Since the value of x is unknown, INSUFFICIENT.
Statement 2: More than 3/5 of the birds in the aviary are spotted.
Many grids are possible.
Two examples:
Here, spotted/total = 30/40 = 3/4.
Here, spotted/total = 40/50 = 4/5.
Since the total number of birds can be different values, INSUFFICIENT.
Statements combined:
The grid in Statement 1 indicates that total spotted = x+40 and that total birds = 2x+50.
Since Statement 2 indicates that total spotted is more than 3/5 of the total number of birds, we get:
(x+40)/(2x+50) > 3/5
5x + 200 > 6x + 150
50 > x.
Since x can be different values, the total number of birds cannot be determined.
INSUFFICIENT.
The correct answer is
E.
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