It is currently 19 Oct 2017, 08:16

# STARTING SOON:

Live Chat with Cornell Adcoms in Main Chat Room  |  R1 Interview Invites: MIT Sloan Chat  |  UCLA Anderson Chat  |  Duke Fuqua Chat (EA Decisions)

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Are x and y both positive?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 05 Oct 2008
Posts: 270

Kudos [?]: 538 [0], given: 22

Are x and y both positive? [#permalink]

### Show Tags

29 Jan 2009, 06:21
3
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:21) correct 48% (01:21) wrong based on 112 sessions

### HideShow timer Statistics

Are x and y both positive?

(1) 2x-2y=1
(2) x/y>1

OPEN DISCUSSION OF THIS QUESTION IS HERE: are-x-and-y-both-positive-1-2x-2x-1-2-x-y-63377.html
[Reveal] Spoiler: OA

Kudos [?]: 538 [0], given: 22

SVP
Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1060 [0], given: 5

Location: New York
Re: Are x and y both positive? [#permalink]

### Show Tags

29 Jan 2009, 07:48
study wrote:
Are x and y both positive?

2x - 2y = 1
x/y > 1

1) 2x - 2y = 1

Alone not sufficient

2) x/y > 1
alone not suffcieint
both can be +ve or both can be -ve

combined

2x - 2y = 1

x=2 y=3/2 both +ve
x= -3/2 y= -2 both -ve

not suffcieint

E
_________________

Smiling wins more friends than frowning

Kudos [?]: 1060 [0], given: 5

SVP
Joined: 29 Aug 2007
Posts: 2472

Kudos [?]: 843 [1], given: 19

Re: Are x and y both positive? [#permalink]

### Show Tags

29 Jan 2009, 08:53
1
KUDOS
x2suresh wrote:
study wrote:
Are x and y both positive?

2x - 2y = 1
x/y > 1

1) 2x - 2y = 1

Alone not sufficient

2) x/y > 1
alone not suffcieint
both can be +ve or both can be -ve

combined

2x - 2y = 1

x=2 y=3/2 both +ve
x= -3/2 y= -2 both -ve
not suffcieint

E

lxl cannot be < lyl.

in that case E may me changed into C.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Kudos [?]: 843 [1], given: 19

SVP
Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1060 [0], given: 5

Location: New York
Re: Are x and y both positive? [#permalink]

### Show Tags

29 Jan 2009, 10:12
study wrote:
I too chose E.

x2suresh/gmat tiger, can you please xplain why C?

Thanks.

both x and y can't be -ve

when they both negative.. |x|>|y| (because x/y>1)
in this case stat1 fails 2x-2y=1 --> this is not possible at all
2x-2y ---> always negative.. (when both x and y are -ve)
_________________

Smiling wins more friends than frowning

Kudos [?]: 1060 [0], given: 5

Manager
Joined: 05 Jul 2008
Posts: 136

Kudos [?]: 123 [1], given: 40

GMAT 2: 740 Q51 V38
Re: Are x and y both positive? [#permalink]

### Show Tags

29 Jan 2009, 10:37
1
KUDOS
study wrote:
Are x and y both positive?

2x - 2y = 1
x/y > 1

1. x-y= 1/2
2. (x-y)y>0

C: 1/2*y>0 => y>0
x-y>0 => x>0

C.... http://www.snarkyarchies.com

Kudos [?]: 123 [1], given: 40

SVP
Joined: 17 Jun 2008
Posts: 1534

Kudos [?]: 279 [0], given: 0

Re: Are x and y both positive? [#permalink]

### Show Tags

30 Jan 2009, 01:32
Similar approach in a different flavor.

From stmt1: x - y > 1/2 > 0
Hence, x > y.

Not sufficient as both x and y can be positive or negative.

From stmt2: x/y > 1
Hence, either x > y > 0 or x < y < 0
Hence, insufficient.

Combining stmt1 and stmt2:
x > y > 0. Hence, sufficient.

Kudos [?]: 279 [0], given: 0

Senior Manager
Joined: 05 Oct 2008
Posts: 270

Kudos [?]: 538 [0], given: 22

Re: Are x and y both positive? [#permalink]

### Show Tags

19 Jun 2010, 05:21
DavidArchuleta wrote:
study wrote:
Are x and y both positive?

2x - 2y = 1
x/y > 1

1. x-y= 1/2
2. (x-y)y>0

C: 1/2*y>0 => y>0
x-y>0 => x>0

C.... http://www.snarkyarchies.com

I don't agree with this solution with reference to statement 2, One cannot conveniently multiply both sides of the equation with y assuming y is positive. If y is negative, the inequality sign changes.

Kudos [?]: 538 [0], given: 22

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128863 [0], given: 12183

Re: Are x and y both positive? [#permalink]

### Show Tags

19 Jun 2010, 05:39
Expert's post
1
This post was
BOOKMARKED
study wrote:
DavidArchuleta wrote:
study wrote:
Are x and y both positive?

2x - 2y = 1
x/y > 1

1. x-y= 1/2
2. (x-y)y>0

C: 1/2*y>0 => y>0
x-y>0 => x>0

C.... http://www.snarkyarchies.com

I don't agree with this solution with reference to statement 2, One cannot conveniently multiply both sides of the equation with y assuming y is positive. If y is negative, the inequality sign changes.

There is no multiplication by $$y$$: it should be $$\frac{x}{y}>1$$ --> $$\frac{x}{y}-1>0$$ --> $$\frac{x-y}{y}>0$$ --> as $$x-y=\frac{1}{2}$$ --> $$\frac{1}{2y}>0$$ --> $$y>0$$ --> as $$\frac{x}{y}>1$$, they both have the same sign, thus $$x>0$$.

Complete solution:

Are x and y both positive?

(1) 2x-2y=1
(2) x/y>1

(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.

(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.

(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.

One of the approaches:
$$2x-2y=1$$ --> $$x=y+\frac{1}{2}$$
$$\frac{x}{y}>1$$ --> $$\frac{x-y}{y}>0$$ --> substitute x --> $$\frac{1}{y}>0$$ --> $$y$$ is positive, and as $$x=y+\frac{1}{2}$$, $$x$$ is positive too. Sufficient.

_________________

Kudos [?]: 128863 [0], given: 12183

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16671

Kudos [?]: 273 [0], given: 0

Re: Are x and y both positive? [#permalink]

### Show Tags

23 Apr 2015, 00:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128863 [0], given: 12183

Re: Are x and y both positive? [#permalink]

### Show Tags

23 Apr 2015, 03:12
OPEN DISCUSSION OF THIS QUESTION IS HERE: are-x-and-y-both-positive-1-2x-2x-1-2-x-y-63377.html
_________________

Kudos [?]: 128863 [0], given: 12183

Re: Are x and y both positive?   [#permalink] 23 Apr 2015, 03:12
Display posts from previous: Sort by