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I. Substituting in the equation x=-1

-2(y+3)(-y-3) = 0

This is true if y=-3 or y=3. |y|=3, prime.

This is always true.

II. (xy+3)=0 if, for example, x=3 and y=-1

|y|=1, not prime
x=3, prime

This can be false.

III. (y+3)=0 if y=-3

-3/x can be an integer choosing the prime number 3

This can be false.

Answer A
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I. x = -1
(-1 - 1)(y + 3)(-y + 3) = 0
(y + 3)(y - 3) = 0
y = 3 or y = -3
|y| = 3

Must be true

II. Counterexample with x = 3, y = -1

III. Counterexample with x = 3, y = -3

The answer is A
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I. if x=-1, -2*(y+3)*(-y+3)=0 if y=-3 or y=3 and |y|=3(prime) in both cases. TRUE

II. if x=3, y=-1 this is FALSE

III. if x=3, y=-3 this is FALSE

The correct answer is A
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We are given,
(x-1)*(y+3)*(xy+3) = 0

=> x = 1 OR
=> y = -3. OR
=> xy = -3

Lets go through each statement 1 by 1

Statement 1: If x = -1, |y| is a prime number

=> (-2)*(y+3)*(-y+3) = 0

Case 1: y = -3
=> |y| = 3 which is prime

Case 2: y = 3
=> |y| = 3 is prime

Statement 1 is true

Statement 2: If |y| is not prime, x is not prime

Case 1:
x = 1, y = 4

=> (1-1)*(4+3)*(4+3) = 0

|y| = 4 not prime and x not prime

Case 2:
x = 3 , y = -1

=>(3-1)*(-1+3)*(-3+3) = 0

Here,
|y| = 1 is not prime and x is prime

So Statement 2 is not true always as both Case 1 and 2 is valid

Statement 3: If x is prime, y/x is not an integer

Case 1:

y = -3 , x = 3

=> x / y = 3 / (-3) = -1 which is an integer

Statement 3 is not true always

A. I only
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(x-1)(y+3)(xy+3) = 0
=> x=1 or y = -3 or xy = -3

Statement 1 : x = -1 |y| is a prime number

If x = -1 then either of the other 2 cases are true
Meaning either y = -3 or (-1)(y) = -3 => y = 3
So |y| = 3 which is a prime number. So must be true statement

Statement 2: if |y| is not a prime , x is not a prime

|y| =/ prime means y cannot be -3. so either of the other 2 statements must be true
X = 1 or xy = -3. If x = 1 it is a prime number. So this statement can be true but not must be true

Statement 3: x is a prime number, y/x is not an integer

X can be 1, 2,3,5 etc. If x = 1, it satisfies the equation while y can be any number.
y/x may or may not be an integer. This statement can be true but is not a must be true.


Answer A
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since product = 0, at least one factor must be 0:

x = 1, or y = -3, or xy = -3

i) x = -1

then y = -3 or 3, so |y| = 3, which is prime.

true

ii) take x = 3 and y = -1.

xy = -3, so eq works. but |y| = 1 is not prime, while x = 3 is prime.

false

iii) take x = 3 and y = -3.

eq works because y + 3 = 0. y/x = -1, which is an int.

false

only i must be true.

ans: a

Bunuel
If x and y are integers and (x - 1)(y + 3)(xy + 3) = 0, which of the following must be true?

I. If x = -1, |y| is a prime number
II. If |y| is not a prime number, x is not a prime number
III. If x is a prime number, y/x is not an integer

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


 


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(x-1) (y+3) (xy+3) = 0

1. If x is -1, y has to be 3 or -3 i.e. mod y = 3
Correct.

2. If y is not prime, lets say -1, then x =1 or x=3 which is prime. Hence this is not always true.

3. If x=2, then y = -3 or -3/2
For first case y/x is -3/2 , not an integer
For second case, y/x is -3/2 by 2 which is -3, which is integer. Hence this is also not always true.

(A) is the answer.
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Bunuel
Could you have a look at this please
https://gmatclub.com/forum/gmat-club-wo ... l#p3808325

Got the kudos here but the points werent added which is a bit unusual
Due to the cloudflare issue, it was posted later
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Mardee
Bunuel
Could you have a look at this please
https://gmatclub.com/forum/gmat-club-wo ... l#p3808325

Got the kudos here but the points werent added which is a bit unusual
Due to the cloudflare issue, it was posted later
We need some time to do that. Thank you for your patience.
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