kaudes11114 wrote:The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
A. 17
B. 16
C. 15
D. 14
E. 13
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If the sum of 3 different perfect squares is 75, each must be less than 75. So, we want to start by writing out the perfect squares that are less than 75:
1, 4, 9, 16, 25, 36, 49, 64
In this problem, there is no shortcut to determining which 3 squares add up to 75; however, it is strategic to start with the largest one, 64, and move down the list if it doesn't work:
64 + 11 = 75
There is no way 11 can be written as a sum of two squares. So, we move down to 49:
49 + 26 = 75
We see that 26 can be written as the sum of 25 and 1; that is:
49 + 25 + 1 = 75
We have found the three perfect squares that sum to 75. In other words:
7^2 + 5^2 + 1^2 = 75
The sum of 7, 5, and 1 is 7 + 5 + 1 = 13.
Answer:
E
