wiut wrote:A number of eggs dyed various colors were hidden for an egg hunt. How many eggs in total were hidden?
1. The number of red eggs hidden was the square of an integer, while the total number of eggs hidden was 24 times that integer.
2. Exactly 143 of the eggs hidden were not red.
Say, total number of eggs = E
Statement 1: The number of red eggs hidden was the square of an integer, while the total number of eggs hidden was 24 times that integer.
Say, number of red eggs = n², where n is an integer and number of eggs which are not red = x.
Therefore, E = 24*n and E = (n² + x)
Thus, (n² + x) = 24*n
=> (n² - 24n + x) = 0
Depending upon the value of x, there can be different values of n and so different values of E.
Not sufficient.
Statement 2: Exactly 143 of the eggs hidden were not red.
We don't know the number of eggs which are red.
Not sufficient.
1 & 2 Together: x = 143
Hence, (n² - 24n + 143) = 0
=> (n² - 11n - 13n + 11*13) = 0
=> (n - 11)(n - 13) = 0
Thus value of n can be either 11 or 13.
Accordingly there are two possible values of E.
Not sufficient
The correct answer is E.
