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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The number 75 can be written as
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kaudes11114
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theCodeToGMAT
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75 = a^2 + b^2 + c^2
To find: a + b + c
If we try Hit and try method by considering that 9^2 > 75. that means we need to find combination lower than 9
8^2 doesn't satisfy
7^2 = 49 ==> 75 - 49 ==> 26 = 25 + 1 = (5)^2 + (1)^2
so, a + b + c = 7 + 5 + 1 = 13
[spoiler]{E}[/spoiler]
To find: a + b + c
If we try Hit and try method by considering that 9^2 > 75. that means we need to find combination lower than 9
8^2 doesn't satisfy
7^2 = 49 ==> 75 - 49 ==> 26 = 25 + 1 = (5)^2 + (1)^2
so, a + b + c = 7 + 5 + 1 = 13
[spoiler]{E}[/spoiler]
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Brent@GMATPrepNow
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We're looking for 3 DIFFERENT squares that add to 75kaudes11114 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
Here are the only squares we need to consider: 1, 4, 9, 16, 25, 36, 49, 64
Can you find 3 that add to 75?
After some fiddling, we may notice that 1 + 25 + 49
In other words, 1² + 5² + 7² = 75
We want the SUM of 1 + 5 + 7, which is 13
Answer: E
Cheers,
Brent
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Matt@VeritasPrep
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I like Brent's way better than the one I'm about to give, but here's another approach.
We know that 25 + 25 + 25 = 75. 25 = 5², so we can guess that ONE of our unique integers is 5. Now we just need to find two that sum to 50. 7² is close, and hey, 1² + 7² is the difference!
Feels a little goofy, but this is how you solve these sort of problems ...
We know that 25 + 25 + 25 = 75. 25 = 5², so we can guess that ONE of our unique integers is 5. Now we just need to find two that sum to 50. 7² is close, and hey, 1² + 7² is the difference!
Feels a little goofy, but this is how you solve these sort of problems ...
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Jeff@TargetTestPrep
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\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
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
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