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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards