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

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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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