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The sum of the squares of two prime numbers is 173. What is

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by Max@Math Revolution » Tue Jul 30, 2019 12:20 am
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[GMAT math practice question]

The sum of the squares of two prime numbers is 173. What is the sum of the two prime numbers?

A. 5
B. 8
C. 10
D. 15
E. 16
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by Brent@GMATPrepNow » Tue Jul 30, 2019 5:38 am
Max@Math Revolution wrote:[GMAT math practice question]

The sum of the squares of two prime numbers is 173. What is the sum of the two prime numbers?

A. 5
B. 8
C. 10
D. 15
E. 16
\
Let x and y be the two primes.
So, x² + y² = 173

Since the sum of the squares is ODD, we know that one square must be EVEN, and the other square must be ODD.
Since 2 is the only even prime, the only way for the square of a prime to be even is when that prime is 2.
Let's say x = 2
We now have: 2² + y² = 173
In other words: 4 + y² = 173
In other words: y² = 169
Solve: y = 13

So, the sum of the prime numbers = 2 + 13 = 15

Answer: D

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by Max@Math Revolution » Wed Jul 31, 2019 10:51 pm
=>

Let the prime numbers be p and q.
Then p^2 + q^2 =173, and one of p and q must be an even number and the other must be an odd number. Since the unique even prime is 2, we can set p = 2.
Then p^2 + q^2 = 4 + q^2 = 173 and q^2 = 169.
Therefore, q = 13 and p + q = 2 + 13 = 15.

Therefore, D is the answer.
Answer: D
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by Scott@TargetTestPrep » Mon Aug 05, 2019 6:10 pm
Max@Math Revolution wrote:[GMAT math practice question]

The sum of the squares of two prime numbers is 173. What is the sum of the two prime numbers?

A. 5
B. 8
C. 10
D. 15
E. 16
13^2 + 2^2 = 169 + 4 = 173

13 + 2 = 15

Answer: D

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