If xyz ≠ 0, is x > 0?
1) xy > 0
2) xz > 0
Considering Statement (1) alone:
xy > 0.
It means that x and y can be positive or x and y can be negative. Insufficient
Considering statement (2) alone:
xz > 0
It means that x and z can be positive or x and z can be negative. Insufficient
Considering both statements:
All three numbers can be positive or all three numbers can negative. Insufficient
If xyz > 0, is x > 0?
1) xy > 0
2) xz < 0
If xyz > 0 => Either exactly 2 of the valriables are negative or all the variables are positive.
Considering statement (1) alone:
xy > 0 => Both x and y can be positive or neagtive. Insufficient
Considering statement (2) alone:
xz < 0 => One of the x or z is negative. So, x can be positive or negative. Insufficient.
Considering both the statments together:
If xy > 0 and xz < 0
There are two possibilities now.
Case 1: When x and y are positive
If x and y are positive and xz < 0 => z is negative.
This is not possible as the question suggests that xyz > 0
Case 2: When x and y are negative
If x and y are negative and xz < 0 => z is positive.
This works for the question also as xyz > 0. And, it provides a definite information that x is negative. Sufficient
A certain list consists of several different integers. Is the product of all the integers in the list positive?
1) The product of the greatest and the smallest of the integers is positive
2) There is an even number of integers in the list.
If there are more than two numbers in the list, is each of the numbers in the list equal to 0?
1) The product of any two numbers in the list is equal to 0
2) The sum of any two numbers in the list is equal to 0
Is x a negative number?
1) x^{2} is a positive number
2) x*y is not positive
If xy > 0, is x > 0?
1) x  y = 3
2) x^{2} = 9
Correct Answer : D
Explanation : a) if xy= 3, it means x& y are positive then x should be greater than y.
Hence Sufficient.
b) As it is given x>0, whether the x is positive and negative, its value will always be positive (Sufficient)
If xy < 0, is x > 0?
1) x  y = 3
2) x^{2} = 9
Correct Answer : b
Explanation : If x > 0 and xy < 0
that means x will be positive and y will be the negative.
x > 0 {the value of x will be 1,2,3,4......}
a) x  y = 3
This means the value of x is positive and y is negative.
Say x is positive then x>yand y is negative.
(Sufficient)
b) x2 = 9
As it is given value of x is positive,it also satisfies the equation
(Sufficient)
If x y > 0, is x > 0?
1) xy < 0
2) x > y
(a)In the question, it is given xy>0, then xy<0 cannot be correct.
(b) As x > y, then xy will be truely greater than zero.
eg : x =2, y = 1
xy > 0
(2)(1) > 0
2 > 0
If x  y > 0, is x > 0?
1) x > y
2) y > 0
Correct Answer : b
Explanation : xy>0 x>0
1) x>y i.e x is greater than y As it is given x>0 that means x will be positive only.
2) y is greater than zero it will also be positive
For eg : x = 2, y = 1
x  y > 0
2  1> 0
1>0 (boh statements are required to answer the question)
If xyz > 0, is x > 0?
1) xy > xz
2) y < 0
Correct Answer : B
Explanation : (1) XY > 0 means x > 0 and Y > 0 OR X < 0 and Y < 0
So (1) is not sufficient
(2) XZ > 0 means X > 0 and Z > 0 OR X < 0 and Z < 0
So (2) is not sufficient
So if x < 0 then y < 0 and z < 0
=> xyz < 0 which is contrary to what is given in question
=> x > 0
If xyz > 0, is x > 0?
1) xy > xz
2) x > y
If xy > xz, is x > 0?
1) x > y
2) x > z
If xyz < 0, is x < 0?
1) yz < 0
2) xy < 0
If xyz < 0, is x < 0?
1) xy > xz
2) y > 0
If xyz > 0, is x < 0?
1) x > yz
2) xz < 0
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