Is xy 1

Question

Is xy < z?

(1) xyz = 1
(2) xyz^2 > 1

Source: Topgmat

minustark · Answer

1) xy = 1/z. Now if xy =6, z =1/6 and xy > z. Again if, xy = 1/6, z = 6 and xy < z. not sufficient

2) xy > 1/z^2. When, xy = 2. z = 2. xy = z. again when, xy = 3, z =1. xy > z. If, xy = 4, z =8, xy , z. not sufficient.

Together, xy.1/x^2z^2>1. xy > x^2y^2 . so xy is between 0 to 1. since, z is the reciprocal of xy, it will always be greater than xy. sufficient.

C is the answer.

firas92 · Answer

(1) xyz = 1 If x=1, y=1, z=1 ---------- xy=z If x=1, y=1/2, z=2 ---------- xy 1 If x=1, y=1, z=2 ----------- xy1 or xyz(z)>1 Since xyz=1, 1*z>1 or z>1 If z>1 and xyz=1, then xy<1 which means xy

IanStewart · Answer

Statement 1 doesn't differentiate among the letters at all, so is clearly insufficient, and Statement 2 can be true when z^2 is small and xy is big or vice versa. So the answer is C or E. Using both Statements, one standard technique you can use when seeing an equation and an inequality is to substitute. The equation tells us xy = 1/z, so we can substitute "1/z" for "xy" in the inequality: (1/z)(z^2) > 1, so z > 1. If z > 1, and xy = 1/z, then xy < 1, and xy < z, so the answer is C.

mSKR · Answer

Is xy1 xy can be greater than z or z^2 ( 9*1/2*1/2) = Greater but xy1- greater but xy>z not sufficient 1+2: xyz.z>1 xyz= 1 and it means z>1 other case: xyz=1 what if xy is negative then z is also negative but in this case xyz.z can not be greate than 1 so this case is not valid hence if z is only greater than 1 then xy must be less than 1 Sufficient hence C

Is xy < z? (1) xyz = 1 (2) xyz^2 > 1

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