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If x and y are positive integers such that x^2+y^2 is a prim

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mun23
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If x and y are positive integers such that x^2+y^2 is a prim [#permalink] New post   Updated on: 27 Feb 2013, 15:34
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If x and y are positive integers such that x^2+y^2 is a prime number less than 18, what is the value of y?

(1) x^2 + y^2 is a prime number
(2) x^2 - y^2 is a prime number
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E

Originally posted by mun23 on 27 Feb 2013, 14:19.
Last edited by Bunuel on 27 Feb 2013, 15:34, edited 2 times in total.
Edited the question.
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Re: If x and y are positive integers such that x^2+y^2 is a prim [#permalink] New post   27 Feb 2013, 15:39
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mun23 wrote:
If x and y are positive integers such that x^2+y^2 is a prime number less than 18, what is the value of y?

(1) x^2 + y^2 is a prime number
(2) x^2 - y^2 is a prime number


By trial and error:

Case #1.
x^2 + y^2 --> 3^2 + 2^2 = 13 = prime.
x^2 - y^2 --> 3^2 - 2^2 = 5 = prime.

Case #2.
x^2 + y^2 --> 2^2 + 1^2 = 5 = prime.
x^2 - y^2 --> 2^2 - 1^2 = 3 = prime.

Answer: E.
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Re: If x and y are positive integers such that x^2+y^2 is a prim [#permalink] New post   30 Apr 2014, 19:08
Hey Bunuel,
The org question is incorrectly written. Here is the correct question:
If x and y are positive integers such that x^2+y^3 is a prime number less than 18, what is the value of y?

(1) x^2 + y^2 is a prime number
(2) x^2 - y^2 is a prime number
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Re: If x and y are positive integers such that x^2+y^2 is a prim [#permalink] New post   01 May 2014, 10:01
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prsnt11 wrote:
Hey Bunuel,
The org question is incorrectly written. Here is the correct question:
If x and y are positive integers such that x^2+y^3 is a prime number less than 18, what is the value of y?

(1) x^2 + y^2 is a prime number
(2) x^2 - y^2 is a prime number


You could use the same numbers because 3^2 + 2^3 and 2^2 + 1^3 are also primes less than 18.
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Re: If x and y are positive integers such that x^2+y^2 is a prim [#permalink] New post   04 Mar 2017, 04:34
Prompt analysis
x and y are positive integers where x^2 +y^2 <18

superset
the value if y will be one of 1,2,3,4

translation
In order to find y, we need:
1# exact value of y
2# two equation two variable in x and y
3# any other property of y.

statement translation
St 1: x^2 +y^2 is prime number.(x,y) or (y,x) will be (1,4), (1,2), (2,3).INSUFFICIENT
St 2: x^2 -y^2 is prime number. (x,y) will be (3,2) , (2,1). INSUFFICIENT

St 1& St 2: we will get (x,y) be either (2,1) or (3,2). INSUFFICIENT.

Option E
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Re: If x and y are positive integers such that x^2+y^2 is a prim [#permalink] New post   17 Mar 2017, 13:09
Infer - Possible values of sum are 2,3,5,7,9,11,13,17

S-1) x = 2, y = 1 : 4+1 = 5 - Prime and y = 1
or x = 3, y = 2 : 9+8 = 17 and y =2. NS

S-2) x = 5, y = 2: 25-8 =17
or x = 6, y = 5: 36 - 25 = 11. NS

S-T) NS. Answer E
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Re: If x and y are positive integers such that x^2+y^2 is a prim [#permalink] New post   09 Oct 2020, 08:37
mun23 wrote:
If x and y are positive integers such that x^2+y^2 is a prime number less than 18, what is the value of y?

(1) x^2 + y^2 is a prime number
(2) x^2 - y^2 is a prime number


target value of y such that x^2+y^2 prime number <18
#1
x^2 + y^2 is a prime number
1^2+1^2 ; 2
4^2+1^2 ; 17
3^2+2^2 ; 13
value of x,y is not fixed insufficient
#2

x^2-y^2 is prime
(x+y)*(x-y)
( 3+2) (3-2) ; 5
(2+1)*(2-1) ; 2
insufficient
from 1 &2
y cannot be determined
option E sufficient
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Re: If x and y are positive integers such that x^2+y^2 is a prim [#permalink]
09 Oct 2020, 08:37
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Bunuel
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