Is xy

Question

Is  xy < 6  ?

(1)  x < 3  and  -y > -2

(2)  y^2 < 100 ,  \frac{1}{2} < x < \frac{2}{3}

chetan2u · Answer

(1) x < 3 and -y > -2.....y<2 If both x and y are positive, xy<6. If both x and y are negative, say x<-3 and y<-2....x=-4 and y=-10, then xy=40>6 Insuff (2) y^2 < 100......|y|<10 , \frac{1}{2} < x < \frac{2}{3} when y=9.9 and x= \frac{2}{3}.....xy=9.9*\frac{2}{3}=6.6>6 when y=-9 and x= \frac{2}{3}.....xy=-9*\frac{2}{3}=-4<6 Combined 2>y>-10 and \frac{1}{2} < x < \frac{2}{3} (negative y * largest x)

GMATinsight · Answer

Question: Is  xy < 6  ?

Statement 1 :  x < 3  and  -y > -2

i.e x < 3 and y < 2

if both x and y are positive then  xy < 6  BUT

Case 1: x = 2 and y = 1, xy = 2 i.e. Less than 6, YES
Case 2: x = -10 and y = -1, xy = 10 i.e. Greater than 6, NO

NOT SUFFICIENT

Statement 2 :  y^2 < 100 ,  \frac{1}{2} < x < \frac{2}{3}

y^2 < 100  ie.  -10 < y < 10  and  \frac{1}{2} < x < \frac{2}{3}

i.e.  (-10)*(\frac{2}{3}) < x*y < (+10)*(\frac{2}{3})

i.e.  (-6.67) < x*y < (+6.67)

NOT SUFFICIENT

COMBINING THE STATEMENTS

(-6.67) < x*y < (+6)  YES

SUFFICIENT

ANswer: Option C

bumpbot · Answer

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Is xy < 6 ? (1) x < 3 and -y > -2 (2) y^2 < 100, 1/2 < x < 2/3

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