[GMAT math practice question]
If the sum of the squares of two positive integers is 106, what is the sum of the two integers?
A. 13
B. 14
C. 15
D. 16
E. 17
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If the sum of the squares of two positive integers is 106, w
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Max@Math Revolution
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Vincen
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Hello.
This is the way I would solve it:
Nº ---- (Nº)^2
1 ---- 1
2 ---- 4
3 ---- 9
4 ---- 16
5 ---- 25
6 ---- 36
7 ---- 49
8 ---- 64
9 ---- 81
10 ---- 100
The only two squared number whose sum is 106 are: 25 and 81.
Then the numbers are 5 and 9. Hence, 5+9=14.
The correct answer is B.
I'd like to know if is there another way to solve it?
This is the way I would solve it:
Nº ---- (Nº)^2
1 ---- 1
2 ---- 4
3 ---- 9
4 ---- 16
5 ---- 25
6 ---- 36
7 ---- 49
8 ---- 64
9 ---- 81
10 ---- 100
The only two squared number whose sum is 106 are: 25 and 81.
Then the numbers are 5 and 9. Hence, 5+9=14.
The correct answer is B.
I'd like to know if is there another way to solve it?
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Brent@GMATPrepNow
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Your solution is perfect. I can't think of a different approach.Vincen wrote:Hello.
This is the way I would solve it:
Nº ---- (Nº)^2
1 ---- 1
2 ---- 4
3 ---- 9
4 ---- 16
5 ---- 25
6 ---- 36
7 ---- 49
8 ---- 64
9 ---- 81
10 ---- 100
The only two squared number whose sum is 106 are: 25 and 81.
Then the numbers are 5 and 9. Hence, 5+9=14.
The correct answer is B.
I'd like to know if is there another way to solve it?
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Max@Math Revolution
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- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
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=>
x^2 + y^2 = 106.
We can plug-in the numbers from 1 to 10 to find the values of x and y that work.
We find that 9^2 + 5^2 = 81 + 25 = 106. So, the two numbers are 5 and 9, and their sum is 9 + 5 = 14.
Therefore, the answer is B.
Answer: B
x^2 + y^2 = 106.
We can plug-in the numbers from 1 to 10 to find the values of x and y that work.
We find that 9^2 + 5^2 = 81 + 25 = 106. So, the two numbers are 5 and 9, and their sum is 9 + 5 = 14.
Therefore, the answer is B.
Answer: B
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Jeff@TargetTestPrep
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We can determine that 5^2 + 9^2 = 106, so the sum of the two numbers is 5 + 9 = 14.Max@Math Revolution wrote:
If the sum of the squares of two positive integers is 106, what is the sum of the two integers?
A. 13
B. 14
C. 15
D. 16
E. 17
Answer: B
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