Is xy positive? (1) x = y + 1 (2) (x + y)^2

Question

Is xy positive?

(1)  x = y + 1 
(2)  (x + y)^2 < (x - y)^2

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CrackverbalGMAT · Accepted Answer

Q. stem(original): Is x y positive?

Q. Stem rephrased :Are x & y of same signs ?

St(1): x=y+1
This doesn't speak of the signs of x & y.

If y=1 then x=y+1= 2 and answer to the Q. stem is Yes

If y = -0.9 then x = y +1 = -0.9 + 1 = 0.1 and answer to the Q. stem is No

There is no definite answer and hence statement is insufficient. Eliminate A & D.

St(2):(x+y)^2<(x−y)^2

=> x^2 + y^2 +2xy < x^2 + y^2 - 2xy

=> 2xy < -2xy (Add -x^2 + -(y)^2 on both sides)

=> 4xy < 0 (Add 2xy on both sides)

Since 4 is positive , x y must be negative.

Answer to the Question stem is a No.

Eliminate C, E
(option b)

D.S
GMAT SME

chetan2u · Answer

Is xy positive? So we have to find whether x and y have same sign. (1) x = y + 1 If x is 0.5 then y is -0.5 and xy<0. If x>1, then y>0 and xy>0. Insufficient (2) (x + y)^2 < (x - y)^2 x^2+y^2+2xy

Crytiocanalyst · Answer

(1) x = y + 1 x=1 , y=0 xy becomes neither positive nor negative Clearly insufficient (2) (x + y)^2 < (x - y)^2 Simplifying , x^2 +y^2 +2x*y < x^2 +y^2 -2x*y => 4xy<0 =>xy<0 Therefore IMO B

AndrewN · Answer

I considered statement (2) in a different manner from what has been outlined above, perhaps because I was not writing anything down. I thought I would share, just in case others in the community could benefit. (These types of number properties questions are quite common.)

* First, neither  x  nor  y  can be 0, since either quadratic would then be the same as the other, violating the inequality.

* Second, if  x  is positive,  y   must  be negative (a positive plus another positive would be greater when squared than a positive plus a negative); along the same lines, if  x  is negative,  y   must  be positive (a negative plus another negative would be greater when squared than a negative plus a positive, and if both  x  and  y  were negative, the right-hand side of the inequality would be less than the left-hand side).

Putting our two realizations together, we can conclude that  Statement (2) is sufficient , and the answer is (B): a positive-negative product will be negative. (We do not even have to test numbers, although we could.)

- Andrew

thelonghalloween · Answer

Statement 1: x = y + 1 --> Clearly insufficient
Statement 2: This says x and y should be of opposite signs. Therefore sufficient
 
IMO B

Victor19 · Answer

The answer is B.

For xy = positive, both x and y should be of the same sign.

Statement 1 : x=y+1.
x=2, y=1 ---- Satisfies the statement and xy is positive.
x=0, y=-1 --- Satisfies the statement but xy is not positive.
Hence, insufficient.

Statement 2 : (x+y)^2<(x−y)^2
This will happen only when x and y are of different signs. Sub different values for x and y and you will agree that x and y have to be of different signs to satisfy this statement.
Hence, sufficient.

Is xy positive? (1) x = y + 1 (2) (x + y)^2 < (x - y)^2

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