is y>0?

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neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Sun May 09, 2010 4:48 am

If x and y are integers and x>0, is y>0?
1. 7x-2y>0
2. -y<x

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sun May 09, 2010 4:58 am

neoreaves wrote:If x and y are integers and x>0, is y>0?
1. 7x-2y>0
2. -y<x

st 1 :

7x-2y>0

7x >2y
y can be -ve or ve or 0

Insufficient

2.-y<x

x>-y. I am not able to "derive" any relation.
So i tried plugging in values.

Case 1: x = 7 y = 2
so , 7 >-2 (YES)

case 2: X =7 y= -2

so, 7> -(-2)
7>2( YES).

here X can take either a +ve or -ve value. Inconsistent

Pick E!

@Nero bhai...Ur DS is tricky & tuf sometimes... Kindly request you to post OA to clear the backlog!

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rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Sun May 09, 2010 7:07 am

If x and y are integers and x>0, is y>0?
1. 7x-2y>0
2. -y<x

from (1) 7x-2y>0

We only know x > 0 .

Y can be positive OR negative and still satisfy equation 1 .

Insufficient .

2. -y<x -------> x > - y

As proven by "gmatmachoman"

"y" can be positive OR negative "x" being positive . Pick numbers .

Combine (1) and (2)

7x - 2y > 0

x>- y ---------> x + y > 0

Multiply both sides by 7 -------> 7x + 7y > 0

Subtract 1 and 2

7x - 2y > 0
-7x - 7y > 0
-----------------
0 - 9y > 0

- 9y > 0 this is only possible when y < 0 .

Hence I would go for C .

"Know thyself" and "Nothing in excess"

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sun May 09, 2010 7:12 am

Rockey Bhai..wonderful..U opened my eyes...ahhaha!! Seems I forgot the whole thing of option C!!

Wonderful reply!!Thx a lot..actually making mistakes is "also" a nice way of learning.. Provided i do only in my "practicezone BTW"

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rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Sun May 09, 2010 7:27 am

Govi Bhai ,

Seems like its not my day to make mistakes

. Good question BTW !!!

"Know thyself" and "Nothing in excess"

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sun May 09, 2010 7:35 am

hmm very much true...keep posting bro

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neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Sun May 09, 2010 8:47 am

rockey...i must say that was superb

...lets hope we all Beat the GMAT to the ground

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Ashish8: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Jan 23, 2010 9:08 pm; Thanked: 2 times

by Ashish8 » Sun May 09, 2010 9:01 am

rockeyb wrote: Multiply both sides by 7 -------> 7x + 7y > 0

Subtract 1 and 2

7x - 2y > 0
-7x - 7y > 0
-----------------
0 - 9y > 0

- 9y > 0 this is only possible when y < 0 .

Rocky, is this a valid operation? I don't think you can subtract inequlities like that cause at the same time you're multiplying the whole inequlity by -1. Which would make the equation:

-7x -7y < 0

This flips the sign and then a simple addition of the two equations is not possible.

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rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Sun May 09, 2010 9:47 am

Ashish8 wrote:
rockeyb wrote: Multiply both sides by 7 -------> 7x + 7y > 0

Subtract 1 and 2

7x - 2y > 0
-7x - 7y > 0
-----------------
0 - 9y > 0

- 9y > 0 this is only possible when y < 0 .
Rocky, is this a valid operation? I don't think you can subtract inequlities like that cause at the same time you're multiplying the whole inequlity by -1. Which would make the equation:

-7x -7y < 0

This flips the sign and then a simple addition of the two equations is not possible.

Bro ,

I know we can add or subtract inequalities and equations consisting inequalities . Even we can solve simultaneous equations using inequalities .

The only operation which you need to look out for are multiplication and division by negative number as that will flip the inequality sign .

But I can see your point here . But the thing is we are not trying to multiply both sides of the equation , instead we are subtracting one equation from another .

If we multiply both sides by -1 then the sign would flip . In case of adding or subtracting inequalities we just need to line up the inequalities and perform addition and subtraction as we would do with equality sign.

"Know thyself" and "Nothing in excess"

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harshavardhanc: Legendary Member; Posts: 526; Joined: Sat Feb 21, 2009 11:47 pm; Location: India; Thanked: 68 times; GMAT Score:680

by harshavardhanc » Sun May 09, 2010 10:30 am

rockeyb wrote:
Ashish8 wrote:
rockeyb wrote: Multiply both sides by 7 -------> 7x + 7y > 0

Subtract 1 and 2

7x - 2y > 0
-7x - 7y > 0
-----------------
0 - 9y > 0

- 9y > 0 this is only possible when y < 0 .
Rocky, is this a valid operation? I don't think you can subtract inequlities like that cause at the same time you're multiplying the whole inequlity by -1. Which would make the equation:

-7x -7y < 0

This flips the sign and then a simple addition of the two equations is not possible.
Bro ,

I know we can add or subtract inequalities and equations consisting inequalities . Even we can solve simultaneous equations using inequalities .

The only operation which you need to look out for are multiplication and division by negative number as that will flip the inequality sign .

But I can see your point here . But the thing is we are not trying to multiply both sides of the equation , instead we are subtracting one equation from another .

If we multiply both sides by -1 then the sign would flip . In case of adding or subtracting inequalities we just need to line up the inequalities and perform addition and subtraction as we would do with equality sign.

rocky,

we should not subtract the inequalities. Addition is okay if the inequalities have the same sign.

see this :

1) 3 > 0
2) 7 > 0

will (1) - (2) be greater than 0? no.

we can tell that (2) - (1) > 0 BECAUSE we know that 7>3.

But in the inequality, like one above, we are not sure which one is greater because of the variables. Hence, subtraction should not be done.

HTH.

Regards,
Harsha

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sun May 09, 2010 10:31 am

neoreaves wrote:rockey...i must say that was superb ...lets hope we all Beat the GMAT to the ground

Ya bro..certainly it was nice feeling well rockey banged/demystified that one for us! Pranab bhai u rock !!

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nakul_anand: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Fri Oct 09, 2009 4:20 pm; Thanked: 4 times

by nakul_anand » Sun May 09, 2010 10:48 am

Hello,

I am confused between C and E

Let x=4 and y=3

7x-2y = 28-6=22>0
and
-y<x (-3<4)

Let x=4 and y=-3
7x-2y = 28+6 = 34>0
and
-y<x (3<4)

So y can be either positive or negative. Right?

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sun May 09, 2010 10:53 am

nakul_anand wrote:Hello,

I am confused between C and E

Let x=4 and y=3

7x-2y = 28-6=22>0
and
-y<x (-3<4)

Let x=4 and y=-3
7x-2y = 28+6 = 34>0
and
-y<x (3<4)

So y can be either positive or negative. Right?

harsha,
wat u said makes sense very much....!!

so in that case we cant do subtraction of equalities...

R&D on GMAT algorithm:

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Ashish8: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Jan 23, 2010 9:08 pm; Thanked: 2 times

by Ashish8 » Sun May 09, 2010 12:14 pm

With the inequality confusion out of the way. I think the answer should be E.

I did it by picking numbers

x = 2

1. 14 - 2y > 0

y < 7

2. -y < 2

y > -2

Combined together y can be from -1 to 6, when x = 2

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neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Sun May 09, 2010 7:20 pm

hmmm ...ok now on second thought....we can not subtract inequalities as suggested by harsha ...though good thing we are discussing this right now to keep our concepts in check

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