Are x and y both positive? : GMAT Data Sufficiency (DS) - Page 2
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 17:26

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

Manager
Joined: 11 Jan 2006
Posts: 230
Location: Arkansas, US
WE 1: 2.5 yrs in manufacturing
Followers: 1

Kudos [?]: 17 [0], given: 18

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

Show Tags

05 Oct 2006, 20:53
anandsebastin wrote:
Are x and y both positive?
1) 2x-2y = 1
2) x/y >1

1. x-y=1/2 x could be negative and Y could be negative?

EX x= -1 y=-3/2 or
Both x and y could be positive.
EX x = 2 y= 3/2
Insufficient

2. x > Y Insufficient Both could be negative or positive
Combine 1 and 2 both X and Y not sufficient

ex: x =-1/4 & y=-3/4 supports 1 and 2 too. They both could be negative or positive

-(1/4) * -(4/3) is not > 1. Does not satisfy statement 2.

Both conditions satisfied only if both X and Y are positive.

If it's any consolation, I was composing a message to the contrary before I realized the mistake we've made.

The second statement is x/y not x*y...
do u c ur mistake...
_________________

ARISE AWAKE AND REST NOT UNTIL THE GOAL IS ACHIEVED

SVP
Joined: 05 Jul 2006
Posts: 1743
Followers: 6

Kudos [?]: 317 [0], given: 49

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

Show Tags

06 Oct 2006, 13:10
Are x and y both positive?
1) 2x-2y = 1
2) x/y >1

from one

x-y = 1/2

thus x,y might be positive 1-1/2 = 1/2 AND /X/>/Y/

or x+ve and y -ve 1/4 -(-1/4) = 1/2 AND /X/<=/Y/

or x -ve and y -ve -1/4 - (-3/4) = 1/2 AND /X/</Y/

from two both have same signe.........INSUFF

BOTH

so they could be both -ve or both positive but /x/>/y / ie(x/y>1)

this is only true if both are positive

edited to delete a rpeated letter
Manager
Joined: 11 Jan 2006
Posts: 230
Location: Arkansas, US
WE 1: 2.5 yrs in manufacturing
Followers: 1

Kudos [?]: 17 [0], given: 18

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

Show Tags

07 Oct 2006, 17:54
I've just worked it out...

the second condition states that, both have to b positive or both have to be negative...

the first condition states that x-y=0.5

the 2 conditions can be satisfied with both x=1, y=0.5
and x =-1, x =-1.5

(but jus a small confusion, the second condition, when seen as the ration x/y>1, is not holding with my second set of numbers, whereas its holding when it is viewed as x>y)

Could any math gurus plzz explain this out...
_________________

ARISE AWAKE AND REST NOT UNTIL THE GOAL IS ACHIEVED

Intern
Joined: 28 Mar 2014
Posts: 23
Location: India
GPA: 3
Followers: 0

Kudos [?]: 8 [0], given: 17

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

Show Tags

25 Jun 2014, 19:20
I tried to solve this question using graphs.
I) 2x-2y = 1 can be written as y = x-1/2. That means its a line having slope of 1 and making y intercept as -1/2. So this line if we see passes through Ist , III and IV quadrant giving different x and y values viz. Ist quadrant x = +, y = +. III quadrant both x & y -ive, IV quadrant x = +ive and y = ive. So obviously I is insufficient.

II ) x/y > 1 means either both x and y are +ive or -ive. Clearly insufficient.

III) Combining the two, we get that either it is in I quadrant or in III quadrant. But in third quadrant the value of y intercept is -1/2 & slope is 1 so the |y| > |x|. So x/y can not be > 1 in third quadrant. While in Ist quadrant x intercept is 1/2 and slope of line is 1 so x>y. therefore Ist quadrant value satisfies giving both x and y as positive.

Is there any flaw in my reasoning.
Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Followers: 43

Kudos [?]: 698 [0], given: 723

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

Show Tags

25 Jun 2014, 20:50
nitin1negi wrote:
I tried to solve this question using graphs.
I) 2x-2y = 1 can be written as y = x-1/2. That means its a line having slope of 1 and making y intercept as -1/2. So this line if we see passes through Ist , III and IV quadrant giving different x and y values viz. Ist quadrant x = +, y = +. III quadrant both x & y -ive, IV quadrant x = +ive and y = ive. So obviously I is insufficient.

II ) x/y > 1 means either both x and y are +ive or -ive. Clearly insufficient.

III) Combining the two, we get that either it is in I quadrant or in III quadrant. But in third quadrant the value of y intercept is -1/2 & slope is 1 so the |y| > |x|. So x/y can not be > 1 in third quadrant. While in Ist quadrant x intercept is 1/2 and slope of line is 1 so x>y. therefore Ist quadrant value satisfies giving both x and y as positive.

Is there any flaw in my reasoning.

Absolutely no flaw...There are many ways to come to the right answer but choose the one method you are more comfortable with....
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93364 [0], given: 10557

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

Show Tags

26 Jun 2014, 00:07
Are x and y both positive?

(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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: are-x-and-y-both-positive-1-2x-2x-1-2-x-y-63377.html
_________________
Re: Are x and y both positive?   [#permalink] 26 Jun 2014, 00:07

Go to page   Previous    1   2   [ 26 posts ]

Similar topics Replies Last post
Similar
Topics:
1 Are x and y both positive? 2 30 Aug 2016, 19:18
1 Are x and y both positive? 1 26 Aug 2016, 03:09
2 Are x and y both positive? 2 19 May 2015, 00:51
11 Are both x and y positive? 16 09 Oct 2013, 22:36
6 Are x and y both positive? 9 29 Jan 2009, 05:21
Display posts from previous: Sort by