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Re: Gprep DS: Is xy>o? [#permalink]
25 Dec 2009, 05:22

2

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Expert's post

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logan wrote:

hi lagomez,

nice method, but i m afraid there is some mistake in ur explanation.

if y>4. say y=5 now plugging this value in eq2, i.e. option 2

x-2y < -6 ===> x-10<-6 ===> x<4 ===> so x can also be -ve... in this case xy<0

plugging the value of y=5 in eq1, i.e. option 1

x-y > -2 ===> x>y+2 ===> x>7 ===> x=+ve.... in this case xy>0

two answers. hence data insuff. Answer:E

here is my method.. as u know, 1 & 2 are individually insuff.. taking 1&2 together

x-y>-2 ===> x>y+2 x-2y<-6 ===> x<2y-6

so combining both the above equations (y+2)< x < (2y-6)

by plugging values, if y= 2 ==> 4<x<-2 ==> x<-2 & x>4 two cases arise. so, data insuff. Answer: E

Not so. Lagomez's answer is correct.

Is xy>0?

(1) x-y > -2 (2) x-2y <-6

Note that question basically asks whether \(x\) and \(y\) have the same sign.

Statements alone are not sufficient as was shown above.

Now, remember we can subtract inequalities with the signs in opposite direction.

\(x-y-(x-2y)>-2-(-6)\) --> \(y>4\). As \(y>4\) and (from 1) \(x>y-2\), hence \(x>2\) (we can add inequalities when their signs are in the same direction, so \(y+x>4+y-2\) --> \(x>2\)) --> both \(x\) and \(y\) are positive. Sufficient.

Answer: C.

When you got that for y=5 --> x<4, it's correct, but it doesn't mean that x can be negative, as this is not ALL information you have. If you plug the same value y=5 in (1) you'll get --> x>3, which is also correct.

Re: Gprep DS: Is xy>o? [#permalink]
25 Dec 2009, 05:51

Expert's post

chetan2u wrote:

i think ans should be E... agreed y>4.. substitute in eq 1...x>2... substitute in eq 2... x<2y-6...x<8-6...x<2..... combining the two , can we get a value of x, which is both < 2 and>2,, i dont think

When you substitute in equation 2, you take the value of y=4 (which can not be as y>4).

Re: Gprep DS: Is xy>o? [#permalink]
25 Dec 2009, 10:34

Bunuel wrote:

Not so. Lagomez's answer is correct.

Is xy>0? (1) x-y > -2 (2) x-2y <-6

Statements alone are not sufficient as was shown above.

Now, remember we can subtract inequalities with the signs in opposite direction.

x-y-(x-2y)>-2-(-6) --> y>4. As y>4 and (from 1) x>y-2, hence x>2. Sufficient.

Answer: C.

When you got that for y=5 --> x<4, it's correct, but it doesn't mean that x can be negative, as this is not ALL information you have. If you plug the same value y=5 in (1) you'll get --> x>3, which is also correct.

Basically when y=5 --> 3<x<4.

Hope it's clear.

oh yeah... too bad that i forgot to plug the value of y=5 in both the equations... thanx a ton Bunuel... kudos.. _________________

Re: Gprep DS: Is xy>o? [#permalink]
01 Jan 2010, 11:28

Bunuel wrote:

chetan2u wrote:

i think ans should be E... agreed y>4.. substitute in eq 1...x>2... substitute in eq 2... x<2y-6...x<8-6...x<2..... combining the two , can we get a value of x, which is both < 2 and>2,, i dont think

When you substitute in equation 2, you take the value of y=4 (which can not be as y>4).

C is correct.

If I substituted x=2 into each of the equations to solve for Y, i got two different answers. Y>4 and Y<4, depending on which equation you substitute it into.

Re: Gprep DS: Is xy>o? [#permalink]
01 Jan 2010, 16:04

lagomez wrote:

4test1 wrote:

Can't seem to find this in the forum. From the Gprep test:

Is xy>0? 1. x-y > -2 2. x-2y <-6

Can't seem to get my head around this. Appreciate any help.

answer c Statement 1: x = 5 and y = 4 answer is yes x = -1 and y = 0 answer is no

Statement 2: x = -7 and y = 0 answer is no x = -10 and y = -1 answer is yes

Combined: x - y > -2 x - 2y < -6

or -x + y < 2 x - 2y < - 6 -y < -4 y > 4 so you know y is positive

What about x..plug a value of y > 4 in the equation and you'll get x > 0

Correct answer is C...

As pointed by Bunuel, when u plug in y > 4 in both the above equations, you get x range as 3<x<4.... Therefore xy > 0!

You shouldn't consider only x - 2y < -6 for determining the value of x. Both the equations should be considered!

Cheers! JT _________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Re: Gprep DS: Is xy>o? [#permalink]
01 Jan 2010, 16:08

Expert's post

burnttwinky wrote:

Bunuel wrote:

chetan2u wrote:

i think ans should be E... agreed y>4.. substitute in eq 1...x>2... substitute in eq 2... x<2y-6...x<8-6...x<2..... combining the two , can we get a value of x, which is both < 2 and>2,, i dont think

When you substitute in equation 2, you take the value of y=4 (which can not be as y>4).

C is correct.

If I substituted x=2 into each of the equations to solve for Y, i got two different answers. Y>4 and Y<4, depending on which equation you substitute it into.

I don't quite understand what's your point. Answer to the original question is C.

xy>0 means that the point (x,y) is either in I quadrant or in III.

(1) x-y > -2 the points satisfying this inequality can be in ALL four quadrants, refer to the first graph msunny provided (blue area). Hence insufficient.

(2) x-2y <-6 the points satisfying this inequality can be in I, II or in III quadrants, refer to the second graph msunny provided (blue area). Hence insufficient.

(1)+(2) Points satisfying BOTH inequalities are only in I quadrant: intersection of blue areas. Hence sufficient.

Re: Gprep DS: Is xy>o? [#permalink]
01 Jan 2010, 16:49

I apologize if my point is unclear, but my question is that, after I calculated X>2 (I solved for X first), I plugged in X=2 into the first equation, and I got Y<4. What I am confused about is that if Y<4, that means Y can be negative; however, x>2, so if Y is negative and X is always positive, then you would be in quadrant IV.

If plugged in X=2 into the second equation, then you get y>4, which is sufficient since X>2 and Y>4, so you will always be in quadrant I.

Re: Gprep DS: Is xy>o? [#permalink]
01 Jan 2010, 17:01

burnttwinky wrote:

I apologize if my point is unclear, but my question is that, after I calculated X>2 (I solved for X first), I plugged in X=2 into the first equation, and I got Y<4. What I am confused about is that if Y<4, that means Y can be negative; however, x>2, so if Y is negative and X is always positive, then you would be in quadrant IV.

If plugged in X=2 into the second equation, then you get y>4, which is sufficient since X>2 and Y>4, so you will always be in quadrant I.

Your X value is > 2, do not substitute 2 as X in the equation. Substituting X = 3 would be a right approach. On doing that for first eq, you get: 3-y>-2 i.e. y < 5 --- [1] Substituting X = 3 in equation 2, you get:

3-2y<-6 i.e. y > 4.5....

Therefore if X = 3, then y range is from 4.5 to 5 which means both X and Y are positive. Hence XY > 0.

Hope this is clear..

Thanks, JT _________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Re: Gprep DS: Is xy>o? [#permalink]
01 Jan 2010, 17:16

Expert's post

burnttwinky wrote:

I apologize if my point is unclear, but my question is that, after I calculated X>2 (I solved for X first), I plugged in X=2 into the first equation, and I got Y<4. What I am confused about is that if Y<4, that means Y can be negative; however, x>2, so if Y is negative and X is always positive, then you would be in quadrant IV.

If plugged in X=2 into the second equation, then you get y>4, which is sufficient since X>2 and Y>4, so you will always be in quadrant I.

First of all when you solved system of inequalities and got x>2 and you want to continue by number plugging you should plug correct numbers. You got x>2, hence you should plug x more than 2. Any value more than 2 for x will give you the RANGE for y which is positive.

You'll get only positive range for y, when you test ANY value of x>2, as the solution of this system of inequalities is x>2 and y>4 (refer to the solution in my first post in this topic). And vise-versa: if you try values of y>4 you'll get only positive range for x.

Re: Gprep DS: Is xy>o? [#permalink]
20 Dec 2010, 02:01

1

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Expert's post

thangvietnam wrote:

you are wrong.

we CAN NOT ADD INEQUALITY, though we can add equality.

a>b and c>d

we can not have a+c>b+d . because there is some redundant

we use this method

y-2<x<2y-6 y-2<2y-6 4<y that means x>2, C is correct.

The red part is not correct.

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\). Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

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