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If the sum of the squares of two positive integers is 106, w

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by Max@Math Revolution » Fri Apr 20, 2018 12:43 am

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[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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by Vincen » Fri Apr 20, 2018 2:40 am
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?
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by Brent@GMATPrepNow » Fri Apr 20, 2018 5:45 am
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?
Your solution is perfect. I can't think of a different approach.

Cheers,
Brent
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by Max@Math Revolution » Sun Apr 22, 2018 5:22 pm
=>
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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by Jeff@TargetTestPrep » Mon Apr 23, 2018 4:47 pm
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
We can determine that 5^2 + 9^2 = 106, so the sum of the two numbers is 5 + 9 = 14.

Answer: B

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