It is currently 19 Mar 2018, 05:56

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

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 883
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

06 Sep 2015, 00:52
Bunuel wrote:
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.

Discussed here: ds1-93964.html?hilit=number%20plugging%20consider%20approaches and also here along with other hard inequality problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.

How do you form these terms in the underlined part? from x/y>1 to x-y/y > 0 ? I do not understand this concept. Thanks.
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Math Expert
Joined: 02 Sep 2009
Posts: 44319
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

06 Sep 2015, 04:20
reto wrote:
Bunuel wrote:
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.

Discussed here: ds1-93964.html?hilit=number%20plugging%20consider%20approaches and also here along with other hard inequality problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.

How do you form these terms in the underlined part? from x/y>1 to x-y/y > 0 ? I do not understand this concept. Thanks.

This is basic:

$$\frac{x}{y}>1$$;

$$\frac{x}{y}-1>0$$;

$$\frac{x}{y}-\frac{y}{y}>0$$;

$$\frac{x-y}{y}>0$$.

Was explained here: are-x-and-y-both-positive-1-2x-2x-1-2-x-y-63377.html#p1060399
_________________
Current Student
Joined: 20 Mar 2014
Posts: 2686
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

06 Sep 2015, 05:13
reto wrote:
Bunuel wrote:
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.

Discussed here: ds1-93964.html?hilit=number%20plugging%20consider%20approaches and also here along with other hard inequality problems: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope it helps.

How do you form these terms in the underlined part? from x/y>1 to x-y/y > 0 ? I do not understand this concept. Thanks.

reto, look below:

You get from statement 1, 2x-2y=1 ---> $$x=\frac{1+2y}{2}$$.....(1)

From statement 2, $$\frac{x}{y} >1$$---> $$\frac{x}{y}-1>0$$ --->$$\frac{x-y}{y} > 0$$ , now substitute for x from (1) above, you get,

$$\frac{\frac{1+2y}{2} -y}{y} > 0$$ ---> $$\frac{\frac{1+2y-2y}{2}}{y} > 0$$ ----> $$\frac{1}{2y} >0$$ ---> $$\frac{1}{y} >0$$ ---> $$y >0$$and as from (1),

$$x=\frac{1+2y}{2}$$, for y>0, x>0 as well.

Alternately, you can view it as:

$$\frac{x}{y} >1$$ ---> x and y both have the same sign (i.e. both of them are either <0 or >0). x>0 ---> y >0 and when x<0 ---> y <0 and vice versa. This is true when $$\frac{x}{y} > 0$$

$$\frac{x}{y} <1$$ ---> x and y both have different sign i.e. x>0 ---> y <0 and when x<0 ---> y >0 and vice versa. This is true when $$\frac{x}{y} < 0$$
Hope this helps.
Intern
Joined: 01 Jul 2015
Posts: 17
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

06 Sep 2015, 20:31
Hi Bunuel
I understoof your line of solving this question.
But just wanted to say in GMAT two statements cannot contradict each other.
Statement 1 says that slope of line is 1, which means x and y co-ordinates will always have same value, which means the ratio x/y = 1 always.
However statement 2 says that x/y>1, how is this possible. This contradicts statement 1.
Correct me if I am wrong.
Current Student
Joined: 20 Mar 2014
Posts: 2686
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

06 Sep 2015, 20:48
Shreeya24 wrote:
Hi Bunuel
I understoof your line of solving this question.
But just wanted to say in GMAT two statements cannot contradict each other.
Statement 1 says that slope of line is 1, which means x and y co-ordinates will always have same value, which means the ratio x/y = 1 always.
However statement 2 says that x/y>1, how is this possible. This contradicts statement 1.
Correct me if I am wrong.

You are correct in saying that 2x-2y=1 has slope of 1 but it is not a must that this statement means that x/y = 1. Having slope of 1 does not mean that the x and y coordinates will be equal (to make x/y =1).

You can confirm this by looking at the set of values satisfying the above equation:

(1.5,1)
(2.5,2)
(3,2.5)

So you see that none of these sets mean x/y > 1.

But your understanding that an official DS question will never have contradictory statements is correct. Though this is not the case for this question.

Hope this helps.
Intern
Joined: 04 Dec 2014
Posts: 12
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

24 Sep 2015, 16:00
What happens when y = o?

X = 0.5 and y = 0, satisfies i and x/y is indeed > 0 since anything divided by 0 is infinity. But, despite this, y is not positive as it '0'.

Even in this case -

"One of the approaches:
2x−2y=1 --> x=y+12
xy>1 --> x−yy>0 --> substitute x --> 1y>0 --> y is positive, and as x=y+12, x is positive too. Sufficient."

The moment you assume y = 0, you can easily see that 1/y is infinity that is greater than 0 and hence, satisfies the equation.

Am i missing something. My answer would be 'E'
SVP
Joined: 12 Sep 2015
Posts: 2145
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

24 Sep 2015, 16:16
2
KUDOS
Expert's post
Manbehindthecurtain wrote:
Are x and y both positive?

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

Target question: Are x and y both positive?

Statement 1: 2x - 2y = 1
There are several pairs of numbers that satisfy this condition. Here are two:
Case a: x = 1 and y = 0.5, in which case x and y are both positive
Case b: x = -0.5 and y = -1, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x/y > 1
This tells us that x/y is positive. This means that either x and y are both positive or x and y are both negative. Here are two possible cases:
Case a: x = 4 and y = 2, in which case x and y are both positive
Case b: x = -4 and y = -2, in which case x and y are not both positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2
Statement 1 tells us that 2x - 2y = 1.
Divide both sides by 2 to get: x - y = 1/2
Solve for x to get x = y + 1/2

Now take the statement 2 inequality (x/y > 1) and replace x with y + 1/2 to get:
(y + 1/2)/y > 1
Rewrite as: y/y + (1/2)/y > 1
Simplify: 1 + 1/(2y) > 1
Subtract 1 from both sides: 1/(2y) > 0
If 1/(2y) is positive, then y must be positive.

Statement 2 tells us that either x and y are both positive or x and y are both negative.
Now that we know that y is positive, it must be the case that x and y are both positive
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

SVP
Joined: 12 Sep 2015
Posts: 2145
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

24 Sep 2015, 16:21
2
KUDOS
Expert's post
jitendra31 wrote:
What happens when y = o?
X = 0.5 and y = 0, satisfies i and x/y is indeed > 0 since anything divided by 0 is infinity. But, despite this, y is not positive as it '0'.
'

It may seem that 0.5/0 = infinity, but this is not the case.
If we approach 0 from the positive side, then it looks like 0.5/0 is a REALLY BIG POSITIVE NUMBER
0.5/0.1 = 5
0.5/0.01 = 50
0.5/0.001 = 500
0.5/0.0001 = 5000
0.5/0.00001 = 50000
etc.

But what if we approach 0 from the NEGATIVE side:
0.5/(-0.1) = -5
0.5/(-0.01) = -50
0.5/(-0.001) = -500
0.5/(-0.0001) = -5000
0.5/(-0.00001) = -50000
Here it looks like 0.5/0 will be a REALLY BIG NEGATIVE NUMBER

This is why we say that x/0 is undefined.

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Current Student
Joined: 20 Mar 2014
Posts: 2686
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

24 Sep 2015, 17:05
jitendra31 wrote:
What happens when y = o?

X = 0.5 and y = 0, satisfies i and x/y is indeed > 0 since anything divided by 0 is infinity. But, despite this, y is not positive as it '0'.

Even in this case -

"One of the approaches:
2x−2y=1 --> x=y+1/2
x/y>1 --> x−y/y>0 --> substitute x --> 1/y>0 --> y is positive, and as x=y+1/2, x is positive too. Sufficient."

The moment you assume y = 0, you can easily see that 1/y is infinity that is greater than 0 and hence, satisfies the equation.

Am i missing something. My answer would be 'E'

As a rule for GMAT quant, a/0 = NOT DEFINED and as such you MUST NOT CONSIDER this case. BY definition, infinity can be both + or - . So your logic of using 'infinity' does not stand. Also , as mentioned before by me you should never consider any case with 0 in the denominator. If there is a case that is for example, a/(b-2) = 3 then for GMAT, you must have b $$\neq$$ 2

This is GMAT's rules and hence you have to follow them.
Intern
Joined: 09 Oct 2015
Posts: 48
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jun 2016, 10:05
As per my solution i am getting E. Kindly help me understand where i am going wrong as the OA is 'C'

1. First statement: 2(x)-2(y)=1 --> x-y=0.5

Now two cases:

(a) X=2.5 , y= 2 , difference is 0.5 --> Both are positives
(b) X= -2, y= -2.5 , difference is 0.5 --> both are negatives

Hence insufficient

2. Second statement: (x/y) >1 --> x>y

Both the numbers can be positive or negative hence insuff

1+2 : Both the statements combined

x-y= 0.5 & x>y

Now two cases:

(a) X=2.5 , y= 2 , difference is 0.5 --> Both are positives ( x>y)
(b) X= -2, y= -2.5 --> -2 -(-2.5) is equal to -2 + 2.5 which results into 0.5. Also -2 > -2.5

difference is 0.5 --> both are negatives

This is insuff, hence 'E' should be the answer
Current Student
Joined: 20 Mar 2014
Posts: 2686
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jun 2016, 10:15
1
KUDOS
sgrover18 wrote:
As per my solution i am getting E. Kindly help me understand where i am going wrong as the OA is 'C'

1. First statement: 2(x)-2(y)=1 --> x-y=0.5

Now two cases:

(a) X=2.5 , y= 2 , difference is 0.5 --> Both are positives
(b) X= -2, y= -2.5 , difference is 0.5 --> both are negatives

Hence insufficient

2. Second statement: (x/y) >1 --> x>y

Both the numbers can be positive or negative hence insuff

1+2 : Both the statements combined

x-y= 0.5 & x>y

Now two cases:

(a) X=2.5 , y= 2 , difference is 0.5 --> Both are positives ( x>y)
(b) X= -2, y= -2.5 --> -2 -(-2.5) is equal to -2 + 2.5 which results into 0.5. Also -2 > -2.5

difference is 0.5 --> both are negatives

This is insuff, hence 'E' should be the answer

Couple of things:

1. x/y >1 DOES NOT mean that x>y (think x=-3 and y=-2). It only means that both x and y will be of same sign.

2. When x=-2, y= -2.5, you are going against S2 that x/y >1 , your case makes it the opposite, x/y < 1. This is where you are making a mistake.

By combining the 2 statements, you will get C as the correct answer.
Intern
Joined: 09 Oct 2015
Posts: 48
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jun 2016, 11:20
Engr2012 wrote:
sgrover18 wrote:
As per my solution i am getting E. Kindly help me understand where i am going wrong as the OA is 'C'

1. First statement: 2(x)-2(y)=1 --> x-y=0.5

Now two cases:

(a) X=2.5 , y= 2 , difference is 0.5 --> Both are positives
(b) X= -2, y= -2.5 , difference is 0.5 --> both are negatives

Hence insufficient

2. Second statement: (x/y) >1 --> x>y

Both the numbers can be positive or negative hence insuff

1+2 : Both the statements combined

x-y= 0.5 & x>y

Now two cases:

(a) X=2.5 , y= 2 , difference is 0.5 --> Both are positives ( x>y)
(b) X= -2, y= -2.5 --> -2 -(-2.5) is equal to -2 + 2.5 which results into 0.5. Also -2 > -2.5

difference is 0.5 --> both are negatives

This is insuff, hence 'E' should be the answer

Couple of things:

1. x/y >1 DOES NOT mean that x>y (think x=-3 and y=-2). It only means that both x and y will be of same sign.

2. When x=-2, y= -2.5, you are going against S2 that x/y >1 , your case makes it the opposite, x/y < 1. This is where you are making a mistake.

By combining the 2 statements, you will get C as the correct answer.

Thank you so much ! That makes perfect sense. I guess I forgot the basic rule that if numbers are negative on the either side of the inequality then the sign of the inequality reverses (as you quoted -3<-2)
Manager
Joined: 16 Mar 2016
Posts: 134
Location: France
GMAT 1: 660 Q47 V33
GPA: 3.25
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jun 2016, 12:49
From statement 1 :
2x-2y=1
2*(x-y)=1
x-y=$$\frac{1}{2}$$
x=$$\frac{1}{2}$$+y

So x>y
Not sufficient

From statement 2 :

$$\frac{x}{y}$$>1>0

So, 2 cases :
- x and y > 0 and x>y
- x and y <0 and x<y
Not Sufficient

From statement 1 & 2 combined :

We know that x>y from statement 1
and we know that x and y > 0 from statement 2

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5048
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jun 2016, 21:17
There are 2 variables (x and y) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Since the condition 1) and 2) each has 1 equation, there is high chance that the correct answer is C. Using 1) and 2), from 2(x-y)=1>0 we get 2(x-y)>0, x>y. Using 2), if we multiply both sides by y^2, we get xy>y^2, xy-y^2>0, y(x-y)>0. Since x-y>0, we get y>0. From x>y>0, x>0. The answer is always yes and the condition is sufficient. Hence, the correct answer is C.

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
Attachments

variable approach's answer probability.jpg [ 219.74 KiB | Viewed 1046 times ]

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Senior Manager
Joined: 18 Jan 2010
Posts: 256
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jun 2016, 22:03
Manbehindthecurtain wrote:
Are x and y both positive?

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

Statement 1
2x-2y = 1

x - y = (1/2)

x = 3/2; y = 1 ; both x and y positive

x = 1/4, y = -1/4; x is positive, y is negative

so not sufficient

Statement 2

(x/y) > 1

x = 3/2; y = 1 ; (x/y) is more than 1. both x and y positive

x = -2; y = -1 ; (x/y) is more than 1. both x and y negative

so not sufficient

Combining Statement 1 and 2

x - y = 1/2

x = y+(1/2)

x/y > 1

{y+(1/2)} / y is more than 1

1+(1/2y) > 1

(1/2y) > 0

y has to be positive. because x = y+1/2, so x also has to be positive.

Manager
Joined: 24 May 2014
Posts: 98
Location: India
GMAT 1: 590 Q39 V32
GRE 1: 310 Q159 V151
GRE 2: 312 Q159 V153
GPA: 2.9
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Aug 2016, 08:45
Hey everyone,

Solved this question by simply picking numbers.

St:1 2x-2y=1, x-y = 1/2, Choice 1: x=3, y=2.5 (Satisfies the prompt), Choice 2: x=-3, y=-3.5 (Yields a diff result). NOT SUFFICIENT

St:2 x/y >1, Choice 1 satisfies the prompt, Assumes some negative values (such as x=-5, y=-10) (Yields a diff result). NOT SUFFICIENT.

Combining both: Choice 1 works. Hence, C.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1741
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

27 Oct 2016, 00:26
Manbehindthecurtain wrote:
Are x and y both positive?

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

clearly each aint suff

both

from 2

(x-y)/y >0 and from 1 , x-y = 1/2 , thus 1/2y>0 thus y is +ve and since x/y>1 and y is +ve therefore x is +ve too ... C
Intern
Joined: 14 Aug 2016
Posts: 2
Location: India
WE: Consulting (Consulting)
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

27 Oct 2016, 01:01
Manbehindthecurtain wrote:
Are x and y both positive?

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

1. 2x-2y = 1 ==> x= y +(1/2) ......[1]
not suuficient

2. x/y>1 ==> x/y>1 .....[2]
not sufficient

combining,

replace x from [1] into [2]

(y+(1/2))/y > 1,

==> 1/y>2 ==> y is positive,
as x>y [from [2]], x is also positive.

Therefore, option C
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2116
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

27 Oct 2016, 17:16
2
KUDOS
Expert's post
Manbehindthecurtain wrote:
Are x and y both positive?

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

Solution:

We need to determine whether x and y are both positive.

Statement One Alone:

2x – 2y = 1

Simplifying statement one we have:

2(x – y) = 1

x – y = ½

The information in statement one is not sufficient to determine whether x and y are both positive. For example, if x = 1 and y = ½, x and y are both positive; however, if x = -1/2 and y = -1, x and y are both negative. We can eliminate answer choices A and D.

Statement Two Alone:

x/y> 1

Using the information in statement two, we see that x and y can both be positive or both be negative. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two, we know that x – y = ½ and that x/y > 1. Isolating x in the equation we have: x = ½ + y. We can now substitute ½ + y for x in the inequality x/y > 1 and we have:

(1/2 + y)/y > 1

(1/2)/y + y/y > 1

1/(2y) + 1 > 1

1/(2y) > 0

Thus, y must be greater than zero. Since x = ½ + y, x also must be greater than zero.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Current Student
Joined: 23 Jan 2016
Posts: 13
GMAT 1: 640 Q36 V40
GMAT 2: 650 Q41 V38
GMAT 3: 710 Q47 V41
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

11 Nov 2016, 21:56
I solved this using a combination of logic and testing general cases.

For (1), think of x-y = 1/2 as the difference between two points on the number line. This difference can occur at if
1. x and y = + (AND x>y)
2. x and y = - (AND y>x)
3. x = +, y= - (AND x>y)

Clearly not sufficient.

(2) tells us that x and y have the same sign AND y>x. Also not sufficient on it's own.

Finally, using (2) we can rule out the first and third options for (1) and you end up with C as the answer.
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1   [#permalink] 11 Nov 2016, 21:56

Go to page   Previous    1   2   3   4    Next  [ 80 posts ]

Display posts from previous: Sort by