If z is a positive number, is r^2 + z z^2 + r ?

Question

If z is a positive number, is r^2 + z > z^2 + r ?

(1) r is a negative number.
(2) z is less than 1.

rohit8865 · Answer

is (r^2-z^2)>r-z (r-z)(r+z)>(r-z) (1) no info of z (2) no info of r both statements are insuff combining (r-z)(r+z-1)>0 As 0IzI then r-z<0 && ((r+z-1)<0 if IrI=IzI then r-z<0 && ((r+z-1)<0 Hence suff Ans C

saurabhsavant · Answer

Do U have an alternate approach? I didnt get ur solution..thanx

Bunuel · Answer

If z is a positive number, is r^2 + z > z^2 + r ? Is r^2 + z > z^2 + r ? Is r^2 - r > z^2 - z? (1) r is a negative number --> r^2 - r = positive - (negative) = positive + positive = positive. So we know that the LHS is positive. We don't know about the RHS. Not sufficient. (2) z is less than 1 --> --> since given in the stem that z is positive, then 0 < z < 1. Notice that in this range z^2 < z (for example, (1/2)^2 < 1/4). Therefore, z^2 - z < 0. We don't know about r^2 - r. Not sufficient. (1)+(2) From above (r^2 - r) = positive > (z^2 - z) = negative. Sufficient. Answer: C. Hope it's clear.

If z is a positive number, is r^2 + z > z^2 + r ?

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If z is a positive number, is r^2 + z > z^2 + r ?

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