chetan2u wrote:

If x and y are integers, is \(\frac{|xy|}{y}\geq{0}\) ?

(1) \(y^3<|y|\)

(2) \(|xy|>|y|\)

self made

Hi

amanvermagmat,

your thinking has been correct but you have neglected the role of second variable x..

lets solve it..

\(\frac{|xy|}{y}\geq{0}\)

the numerator will be 0 if x is 0 OR it will be POSITIVE as the value is in MOD

(1) \(y^3<|y|\)

since y is an integer, y will be a negative integer..

BUT we have x too..

if x is 0, \(\frac{|xy|}{y}={0}\), and ans is YES

If x is an integer, \(\frac{|xy|}{y}<{0}\)... ans is NO

insuff

(2) \(|xy|>|y|\)

square both sides...

\((xy)^2>y^2......y^2(x^2-1)>0\)

although it does not give anything to solve but tells us that both x and y are non zero

insuff

combined-

y is negative and x is non zero

so \(\frac{|xy|}{y}\geq{0}\) is always NO.

C

oh ok! Thanks so much. Kudos!