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

Question

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

Bunuel · Answer

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.

prsnt11 · Answer

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

Bunuel · Answer

You could use the same numbers because 3^2 + 2^ 3  and 2^2 + 1^ 3  are also primes less than 18.

KrishnakumarKA1 · Answer

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

coolkl · Answer

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

Archit3110 · Answer

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

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

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