If x and y are integers, is xy greater than 0? 1) x2 is greater than

Question

If x and y are integers, is xy greater than 0?

(1) x^2 is greater than 0.
(2) y^3 < –9

Kurtosis · Answer

St1: x^2 > 0 --> x can be positive or negative but not equal to 0. Also no information available about y
Not sufficient.

St2: y^3 < -9 --> y < -2. Statement does not provide any information about x.
Not sufficient.

Combining St1 and St2,
If x is +ve and y < -2 --> xy is negative
If x is -ve and y < -2 --> xy is positive
Not sufficient

Answer: E

CV7585 · Answer

If x and y are integers, is xy greater than 0?

(1) x^2 is greater than 0.
(2) y^3 < –9

xy>0? (Only if x and y are both +ve or both -ve).

Statement 1: X^2 >0 (All we can infer is x is not equal to 0)
x could be +ve or -ve. Also no info about y. - Not sufficient.

Statement 2: All we know is y < cube root of -9. no info about x. - Not sufficient.

Statement 1 and 2: We know y is less than cube root of -9, however x could be +ve or -ve. Therefore not sufficient either.

Answer E.

OptimusPrepJanielle · Answer

Before we start solving, remember, -ve number raised to an even power will be positive -ve number raised to an odd power will be negative Is xy > 0? Statement 1: x^2 is greater than 0 Here x > 0 or x < 0 and no information about y. Insufficient Statement 2: y^3 < –9 Hence y will be -ve and no information about x. Insufficient Combining both statements: x > 0 or x < 0 and y < 0 Hence nothing can be said about xy. Insufficient Option E

MathRevolution · Answer

If x and y are integers, is xy greater than 0?

(1) x^2 is greater than 0.
(2) y^3 < –9

There are 2 variables (x,y) in the original condition. In order to match the number of variables to the number of equations, we need 2 more equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer.
Using both the condition 1) and the condition 2), from x^2>0, we get x=/0. So, when x=-1 and y=-3, the answer is yes. When x=1 and y=-3, the answer is no. Therefore, the condition is not sufficient and the correct answer choice is E.

l For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

sameerspice · Answer

1 tells us nothing about x, whether it is +ve or -ve => NOT Sufficient 2. tells that y<= -3, since (-2)^3 = -8 and y^3 < -8. But no information on X => NOT Sufficient Using 1 & 2 together we still can't say anything about sign of X*Y Hence E

If x and y are integers, is xy greater than 0? 1) x2 is greater than

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