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07 Dec 2019, 09:11
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
49% (03:03) correct
51%
(02:32)
wrong
based on 152
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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.
(1) x^2 + y^2 is a prime number.
(2) x^2 – y^2 is a prime number.
07 Dec 2019, 09:39
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x and y are positive integer.
x^2+y^3 is prime less than 18. Least prime no. 2 and highest prime no. 17 for given condition.
St. 1
x^2+y^2 is prime
x= 1, y = 1 will give 2
x= 3, y= 2 will give 13
y = 1 and 2
Not sufficient.
St. 2 x^2-y^2 is prime
(x-y)(x+y), x-y must be 1
So x = 2, y = 1 will give 3
X= 3, y = 2 will 5
y = 1 and 2
Combined st. 1 and 2 will give same results for Y.
E is answer.
x^2+y^3 is prime less than 18. Least prime no. 2 and highest prime no. 17 for given condition.
St. 1
x^2+y^2 is prime
x= 1, y = 1 will give 2
x= 3, y= 2 will give 13
y = 1 and 2
Not sufficient.
St. 2 x^2-y^2 is prime
(x-y)(x+y), x-y must be 1
So x = 2, y = 1 will give 3
X= 3, y = 2 will 5
y = 1 and 2
Combined st. 1 and 2 will give same results for Y.
E is answer.
05 Oct 2020, 07:29
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Raxit85
If x and y are positive integers such that x² + y³ is a prime number less than 18, what is the value of y?
(1) x² + y² is a prime number.
(2) x² – y² is a prime number.
(1) x² + y² is a prime number.
(2) x² – y² is a prime number.
Given: x and y are positive integers such that x² + y³ is a prime number less than 18
There aren't many pairs of values that satisfy the condition x² + y³ is a prime number less than 18
So it might be useful (and faster) to list all possible pairs of values:
case i: x = 1 and y = 1
case ii: x = 2 and y = 1
case iii: x = 3 and y = 2
case iv: x = 4 and y = 1
Target question: What is the value of y?
Statement 1: x² + y² is a prime number
All 4 cases satisfy Statement 1.
So, we can see that EITHER y = 1 or y = 2
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x² – y² is a prime number
Cases ii and iii satisfy Statement 2, which means EITHER y = 1 or y = 2
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Cases ii and iii satisfy BOTH statements, which means EITHER y = 1 or y = 2
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
