If the product of X and Y is a positive number, is the sum of X and Y a negative number?
(1) X > Y5
(2) X > Y6
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Data Sufficiency Number Property
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ajaysingh24
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mathrupradeep
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I think it is E.
Because
1. X>Y5
Case 1 : x=100,y=2 holds true
Case 2 : x=-2, y=-100 holds true
Two possibilities not sufficient.
2. X >Y6
The same cases applied above is applicable even for this.
Even if we combine both it is not possible to tell whether the sum of X and Y is -ve. Hence E.
Because
1. X>Y5
Case 1 : x=100,y=2 holds true
Case 2 : x=-2, y=-100 holds true
Two possibilities not sufficient.
2. X >Y6
The same cases applied above is applicable even for this.
Even if we combine both it is not possible to tell whether the sum of X and Y is -ve. Hence E.
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GMATGuruNY
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The problem should be as follows:
Statement 1: x > y�
Case 1: y=1, x=2
In this case, x+y = 2+1 = 3, which is NOT negative.
Case 2: y=-1, x = -1/2
In this case, x+y = -1/2 + -1 = -3/2, which IS negative.
INSUFFICIENT.
Statement 2: x > y�
Since y≠0, y� > 0.
Thus:
x > y� > 0.
Since x>0, x and y are BOTH POSITIVE.
Thus, x+y > 0.
SUFFICIENT.
The correct answer is B.
Since xy > 0, x and y are either BOTH POSITIVE or BOTH NEGATIVE.If the product of x and y is a positive number, is the sum of x and y a negative number?
(1) x > y�
(2) x > y�
Statement 1: x > y�
Case 1: y=1, x=2
In this case, x+y = 2+1 = 3, which is NOT negative.
Case 2: y=-1, x = -1/2
In this case, x+y = -1/2 + -1 = -3/2, which IS negative.
INSUFFICIENT.
Statement 2: x > y�
Since y≠0, y� > 0.
Thus:
x > y� > 0.
Since x>0, x and y are BOTH POSITIVE.
Thus, x+y > 0.
SUFFICIENT.
The correct answer is B.
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Brent@GMATPrepNow
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IMPORTANT CONCEPTS:ajaysingh24 wrote:If the product of x and y is a positive number, is the sum of x and y a negative number?
(1) x > y^5
(2) x > y^6
An ODD power preserves the sign of the base.
For example, (-5)^3 = -125 and 2^5 = 32
An EVEN power always yields a positive number (as long as the base ≠0
For example, (-5)^4 = 625 and 2^6 = 64
Target question: Is the sum of x and y negative?
Given: the product xy is positive
This tells us that EITHER x and y are both positive, OR x and y are both negative
Also, if the product xy is positive, we know that x ≠0 and y ≠0
Statement 1: x > y^5
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = -1 and y = -2, in which case the sum of x and y IS negative
Case b: x = 10 and y = 1, in which case the sum of x and y is NOT negative
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > y^6
Since y ≠0 we know that y^6 must be positive [since we have an EVEN exponent]
If x > y^6, then we know that x MUST BE POSITIVE
So, there are only 2 possible scenarios to consider:
Scenario #1: x is positive and y is positive
Scenario #2: x is positive and y is negative
HOWEVER, scenario #2 CANNOT OCCUR because it is given that the product xy is positive, and the product cannot be positive in scenario #2.
So, scenario #1 is the only possible scenario, which means x is positive and y is positive, which means the sum of x and y is definitely NOT negative
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
