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# Fun with inequalities

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Intern
Joined: 14 May 2010
Posts: 48

Kudos [?]: 5 [0], given: 8

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07 Jul 2010, 05:42
Hey there

Could you possibly help me with an induction which I couldn't understand, it was off an MGMAT CAT

The questions involves the expression

|x|xy + 9 > 0 // and we will later plaug in -1 for y

I can see how that is the same as

|x|xy > -9

And after plugging in -1, I can see how that becomes

|x|x (-1) > -9

And I can see how after diving by -1, which is a negative number the inequality becomes

|x|x < 9

What I can't get, is that the inequality, according to the solution was not reduced to

|x|x < 9 after division by -1

But instead, it was reduced to

x < 9

BOOOOM !! How did that happen ?

Since we are on this, I identified one of my weak points to be SPECIFICALLY inequalities/modulus in DS questions, how can I improve in this area ?

P.S I am not sure whether this post needs to go here or under Math problems, please let me know so I can make sure it sits in the right place

Kudos [?]: 5 [0], given: 8

Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1915

Kudos [?]: 2204 [0], given: 210

Concentration: General Management, Nonprofit

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07 Jul 2010, 06:59
Do you think you could just post the actual question? Thanks.

Kudos [?]: 2204 [0], given: 210

Intern
Joined: 14 May 2010
Posts: 48

Kudos [?]: 5 [0], given: 8

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07 Jul 2010, 08:39
Hey whiplash, yeah ofcourse

So its a DS question

- If |x|xy + 9 > 0 , and x and y are integers, is x < 6

1) y is negative
2) y <= 1

The inquiry i posted is specifically about MGMAT's explanation for statement one (they happen to chose -1 as an example) and as they were reducing the inequality, they jumped from this

|x|x (-1) > -9

to this

x < 9

as opposed to

|x|x < 9

So I am not sure how they induced that

Thanks a lot

Kudos [?]: 5 [0], given: 8

Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1915

Kudos [?]: 2204 [0], given: 210

Concentration: General Management, Nonprofit

### Show Tags

07 Jul 2010, 09:50
That sounds kind of inconsistent, actually. Maybe it was just a printing mistake?

Kudos [?]: 2204 [0], given: 210

Re: Fun with inequalities   [#permalink] 07 Jul 2010, 09:50
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