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01 Oct 2018, 04:53
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
40% (02:21) correct
60%
(02:16)
wrong
based on 95
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If x and z are positive integers, is at least one of them a prime number?
(1) x^2 = 15 + z^2
(2) (x − z) is a prime number
(1) x^2 = 15 + z^2
(2) (x − z) is a prime number
01 Oct 2018, 05:17
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Bunuel
Question: is at least one of x and z a prime number?
Statement 1:x^2 = 15 + z^2
i.e. \(x^2-z^2 =15\)
i.e. \((x-z)*(x+z) =15\)
i.e. \((x-z)*(x+z) =3*5\) OR
i.e. \((x-z)*(x+z) =1*15\)
If x-z = 3 the x and z may be 5 and 2 both prime OR x and z may be 9 and 6 both NON Prime
NOT SUFFICIENT
Statement 2: (x − z) is a prime number
x-z = 5-3=2 i.e. Both prime OR
x-z = 6-4=2 i.e. None prime
NOT SUFFICIENT
Combining both statements
\((x-z)*(x+z) =15\) and \(x-z\) is prime i.e. either 3 or 5
If x-z = 3 the x and z may be 5 and 2 both prime OR x and z may be 9 and 6 both NON Prime
NOT SUFFICIENT
Answer: Option E
01 Oct 2018, 21:27
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Bunuel
Lets deal with Statement 1 first using plugin approach:
1 x^2 = 15 +z^2
2 we can write above statement as
x^2-Z^2=15 or (x+z)(x-z)=15
3. x+z= 3 means- 1 + 2=3 and x-z means- 4-1
4. so (1,2) and (4,1) -leads to insufficent we have 2 answers
A insufficient
II. Lets move on to 2nd statement
1. x-z is prime number
2. put x=4 , z=1 , none are prime , 4-1=3 , which is prime, so we got 1 no answer
3. put x=5 , y=2, both are prime, 5-2=3, which is prime, so we got 1 yes answer
So clearly B is insufficent
III. combining Statement 1 and statement 2
a)x^2-z^2=15
b) x-z =prime
if you plug values (4,1), both satisfies statement a and b,
if you try value like(5,2) , or any other combination, it wont satisfy both
hence A and B combined are sufficnet
Correct answer: C
Bunuel, please correct my approach if i m wrong
