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# Is xy < 6? (1) x < 3 and y < 2 (2) < x < 2/3

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Joined: 27 Dec 2004
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Is xy < 6? (1) x < 3 and y < 2 (2) < x < 2/3 [#permalink]  31 Mar 2005, 17:38
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Is xy < 6?

(1) x < 3 and y < 2
(2) Â½ < x < 2/3 and y^2 < 64

Please explain your reasoning.
VP
Joined: 25 Nov 2004
Posts: 1495
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Re: DS- [#permalink]  31 Mar 2005, 18:00
B. Resoning left for others or explain later..
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[#permalink]  31 Mar 2005, 22:20
(1) Not sufficient. x can be 1, y can be 1, xy <6. But x can be -2, y can be -5, and xy > 6.

(2) y^2 < 64
y^2-64 < 0
(y+8)(y-8) < 0
-8<y<8

0.5 < x < 0.66

-5.2<xy<5.28

Sufficient.

B it is.
VP
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[#permalink]  02 Apr 2005, 03:37
B too

first statement : take examples :
x=-8 and y=-2 ; xy=16 so xy>6
x=-1 and y=-2 ; xy=2 so xy<6
not suff

second statement :
y<8 or y>-8
1/2<x<2/3
the idea is to find the greatest possible number for x and for y so that we can check if it's reaching numbers above 6
maximum number would be : xy < 2/3*8 ; xy<16/3 ; xy < 5+1/3
xy will always be <6
suff
[#permalink] 02 Apr 2005, 03:37
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# Is xy < 6? (1) x < 3 and y < 2 (2) < x < 2/3

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