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

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Director
Joined: 03 Jun 2009
Posts: 791
Location: New Delhi
WE 1: 5.5 yrs in IT
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Is xy < 6? (1) x < 3 and y < 2 (2) [#permalink]

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07 Jul 2009, 10:40
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$$Is xy < 6?$$

$$(1) x < 3 and y < 2$$

$$(2) 1/2 < x < 2/3 and y^2 < 6$$
_________________
Director
Joined: 03 Jun 2009
Posts: 791
Location: New Delhi
WE 1: 5.5 yrs in IT
Followers: 85

Kudos [?]: 817 [0], given: 56

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07 Jul 2009, 11:51
OA is B.

Great! Thanks for the quick reply. I was making silly mistake of complicating option B by doing all sort of cross-multiplication etc etc, not realising that it can be solved so easily.
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Director
Joined: 03 Jun 2009
Posts: 791
Location: New Delhi
WE 1: 5.5 yrs in IT
Followers: 85

Kudos [?]: 817 [0], given: 56

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07 Jul 2009, 12:21
bigoyal wrote:
try to notice the negative sign for Sqrt 6 in Y, which should be multiplied by the bigger number in the inequality of X (2/3).

Sorry, if this sounds very basic. Any specific reason for that ? Can't we write:
Range = (1/2*-2.45 < xy < 2.45*2/3)

I just thought you are trying to find out the maximum possible values for the product xy.
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Manager
Joined: 28 Jan 2004
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Location: India
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09 Jul 2009, 22:55
B.

Stmt 1 -
Will not hold true if both X and Y are -ve and produc becomes more hen 6.
I mean X=Y= -5 etc.

Stmt 2 -

max. X = LT2 (Less then 2)
min. X = GT.5

max. Y = LT+3
min. Y = GT(-3)

Product of biggest two numbers which we can see (XY) is either LT6 or LT(-6)

Hence suff.
Re: DS- Inequality   [#permalink] 09 Jul 2009, 22:55
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