It is currently 23 Feb 2018, 19:45

### 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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 May 2016
Posts: 2
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jan 2017, 11:47
What about the example of y=0? Then x/y is surely greater than 1, hence I chose answer E.
SVP
Joined: 11 Sep 2015
Posts: 2065
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jan 2017, 12:50
Expert's post
Top Contributor
1
This post was
BOOKMARKED
vgmatv wrote:
What about the example of y=0? Then x/y is surely greater than 1, hence I chose answer E.

x/0 can be really big OR really small...

From my earlier post:

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

Senior Manager
Joined: 23 Feb 2015
Posts: 473
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Mar 2017, 09:14
Manbehindthecurtain wrote:
Are x and y both positive?

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

Statement 1:
2x-2y = 1
IF we get a positive integer (1) when value 2 (2y) is subtracted from value 1 (2x), then it means value 1 is definitely greater than value 2.
That means:
2x>2y
=x>y
Actually statement 1 says that x>y.
now plug in:
5>3------->yes, both are positive.
again,
-3>-5------>no, both are negative.
So, insufficient.

Statement 2:
x/y>1
Now, plug in:
5/3>1---->yes, both are positive
again,
-5/-3>1---->no, both are negative.
So, insufficient.

Now combining statement 1 and statement 2:
x>y----------->Statement 1
x/y>1-------->statement 2
So, plug in:
5/3>1, yes both are positive.
again,
-3/-5>1? does not maintain the statements condition.
again,
5/-3>1?does not maintain the statements condition.
So, The correct choice is C.
Thank you...
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
― Henry Wadsworth Longfellow

Intern
Joined: 03 Aug 2016
Posts: 34
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

07 Jun 2017, 02:19
Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

Sorry for bringing this old question up in the loop. I could see many explanations that used some algebraic inequalities and arrived at the conclusion that Both Statements 1 and 2 are required. I agree that one statement alone will never suffice

But if we take an example such as
x=-0.5 , y=-1 , then statement 1 and 2 (modified to x/y >1 ----> x>y )are both satisfied.
for x=1 and y=0.5 , then statement 1 and 2 (modified to x/y >1 ----> x>y )are both satisfied. So E is correct.
Can someone explain what this discrepancy is ??
Intern
Joined: 09 May 2016
Posts: 46
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

11 Jun 2017, 09:46
Manbehindthecurtain wrote:
Are x and y both positive?

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

mikemcgarry Hi Mike need your advice. I had gone through a solution of yours of using graph to solve inequality which was amazing.I was trying to use similar approach. Can you please help me how C is the right answer by graphical approach. I am getting how statement 1 and 2 by themselves are not sufficient but cannot come upto C
Math Expert
Joined: 02 Sep 2009
Posts: 43892
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

20 Jun 2017, 21:27
TaN1213 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: http://gmatclub.com/forum/ds1-93964.htm ... approaches and also here along with other hard inequality problems: http://gmatclub.com/forum/inequality-an ... 86939.html

Hope it helps.

Hi Buñuel,

If we put x=1/2 & y=0 , would you please explain how are both statements together sufficient? Both statements hold true for these values of x and y, yet 0 is not positive.

Regards.
chris558 wrote:
Are x and y both positive?

1) 2x-2y=1
2(x-y)=1
x-y=1/2
-->3/4-1/4=1/2....YES
-->-1/4-(-3/4)=1/2...NO
INSUFFICIENT

2) x/y>1
This just means that x and y have the same sign. They're either both positive or both negative.
INSUFFICIENT

1&2)
x=1/2+y

(1/2+y)/y>1
y/2 + 1 > 1
y/2 > 0 which means that Y is greater than 0. And since both x and y have the same sign, both x and y are Positive. YES.

Sent from my Redmi Note 4 using GMAT Club Forum mobile app

y cannot be 0 because in this case x/y will not be defined (division by 0 is not allowed) and not greater than 1 as given in the second statement.
_________________
Manager
Joined: 03 May 2017
Posts: 115
Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

21 Jun 2017, 04:44
Jk8269 wrote:
Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

Sorry for bringing this old question up in the loop. I could see many explanations that used some algebraic inequalities and arrived at the conclusion that Both Statements 1 and 2 are required. I agree that one statement alone will never suffice

But if we take an example such as
x=-0.5 , y=-1 , then statement 1 and 2 (modified to x/y >1 ----> x>y )are both satisfied.
for x=1 and y=0.5 , then statement 1 and 2 (modified to x/y >1 ----> x>y )are both satisfied. So E is correct.
Can someone explain what this discrepancy is ??

Hi,

I think the discrepancy is that you are plugging in differents sets of numbers. When you plug in, you have to plug in the same numbers for both statements. IMO, it is better to approach the statements rather than trying to shoehorn them.

In your example, if you stick with the numbers you used for statement 1, then statement 2 will be invalid, i.e -.5/-1 is not >1. Basically, you have changed the prompt.
IMO, the most effective way to solve this problem is a combination of the algebraic and plug-in method. Combining both equations will show that 1/2y > 0, if this is true, then y is positive and if you go back to 1. i.e x=y+.5, with y being positive, x must surely be positive. Hence combining the statements is sufficient, hence C.

Now to plug in requires you to know that the difference between x and y is .5 and that x is the greater number. However, as you rightly suggested, we are not aware of the signs. Yet, statement 2 said x/y -1 >0 . Now intuitively, for this to be consistent x has to be positive because otherwise, the absolute value of x would have to change. And if x is positive, y must be as well.

Plug in examples:

$$x= 1.5 y=1$$, For statement 1, = $$3-2=1$$- correct ; statement 2 = $$\frac{1.5}{1} >1$$correct

$$x= -1, y=-1.5$$, For statement 1, =$$-2+3=1$$- correct ; statement 2 = $$\frac{-1}{-1.5} < 1$$ incorrect

Since all positive values of x and y work. Both statements are definitely sufficient.

Best,

Last edited by rulingbear on 24 Oct 2017, 09:27, edited 5 times in total.
Verbal Forum Moderator
Joined: 19 Mar 2014
Posts: 992
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

21 Jun 2017, 12:36
Are x and y both positive?

(1) 2x-2y = 1

2(x-y) = 1

x-y = 1/2 = 05

Lets substitute some values and check:

x = 0.1 & y = -0.4

0.1 - (-0.4) = 0.5 ==============> Answer to the question is NO

x = 1 & y = 0.5

1 - 05 = 0.5 =================> Answer to the questions is YES

As we are getting multiple answers, Statement (1) is Not Sufficient.

(2) x/y > 1

Which means both x & y have same sing, they can be either positive or both negative.

As we are getting multiple answers, statement (2) us Not Sufficient.

Now, lets combine both (1) and (2)

we get:

x = y + 1/2

also, we know x/y>1

which means: (y+1/2)/y>1

which means y is > 0

as y>0, x has to be > 0 as well. So we can come to the conclusion that both x & y are positive.

Hence, Answer is C

_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Manager
Joined: 05 Nov 2014
Posts: 115
Location: India
Concentration: Strategy, Operations
GMAT 1: 580 Q49 V21
GPA: 3.75
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Jun 2017, 07:33
Are x and y both positive?

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

Solution:

Statement 1: x-y=0..5. So x=1& y=0.5 or x=0& y=-0.5. Therefore insufficient.
Statement 2: x,y can be both positive or both negative.

Combining St1 & St2,
Both the values can't be negative to yield a positive value. Therefore both x & y are positive.

Therefore the answer is Option C.
Manager
Joined: 07 Jun 2017
Posts: 108
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

30 Jul 2017, 02:06
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: http://gmatclub.com/forum/ds1-93964.htm ... approaches and also here along with other hard inequality problems: http://gmatclub.com/forum/inequality-an ... 86939.html

Hope it helps.

How do you get x --> $$\frac{1}{y}>0$$ --> $$y$$ is positive ?
this part really confuse me
Math Expert
Joined: 02 Sep 2009
Posts: 43892
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

30 Jul 2017, 02:09
pclawong 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: http://gmatclub.com/forum/ds1-93964.htm ... approaches and also here along with other hard inequality problems: http://gmatclub.com/forum/inequality-an ... 86939.html

Hope it helps.

How do you get x --> $$\frac{1}{y}>0$$ --> $$y$$ is positive ?
this part really confuse me

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

Positive/y > 0.

y = positive.
_________________
Manager
Joined: 07 Jun 2017
Posts: 108
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

30 Jul 2017, 06:49
Bunuel wrote:
pclawong 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: http://gmatclub.com/forum/ds1-93964.htm ... approaches and also here along with other hard inequality problems: http://gmatclub.com/forum/inequality-an ... 86939.html

Hope it helps.

How do you get x --> $$\frac{1}{y}>0$$ --> $$y$$ is positive ?
this part really confuse me

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

Positive/y > 0.

y = positive.

Thank you for your response.

But my question is , how do you get 1/y from (x-y)/y ?
Math Expert
Joined: 02 Sep 2009
Posts: 43892
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

30 Jul 2017, 10:30
pclawong wrote:
Thank you for your response.

But my question is , how do you get 1/y from (x-y)/y ?

$$\frac{x}{y}>1$$ --> $$\frac{x}{y}-1>$$ --> $$\frac{x-y}{y}>0$$. Now, substitute $$x=y+\frac{1}{2}$$ there to get $$\frac{1}{2y}>0$$, which further simplifies to $$\frac{1}{y}>0$$.

Hope it's clear.
_________________
Manager
Joined: 01 Nov 2016
Posts: 71
Concentration: Technology, Operations
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

16 Aug 2017, 18:10
Bunuel wrote:

So from (2) $$\frac{x}{y}>1$$, we can only deduce that $$x$$ and $$y$$ have the same sigh (either both positive or both negative).

This helped me a lot and gave me an easy way to see the solution.

Statement 1: insufficient, all we have is y = x - 0.5.

Statement 2: insufficient, all we know is that x and y are the same sign (negative/negative or positive/positive), and that x/y > 1.

Combined statements: If we look at the graph of y = x - 0.5, we can see that it is a straight line that goes through quadrant 1, 3, and 4. We can ignore all the values in quadrant 4 because in that quadrant, x and y are different signs. We can ignore the values in quadrant 3, because in that quadrant x/y < 1. Which means that the values must be in quadrant 1, because only there is x/y > 1. Which means x and y are both positive, both statements together are sufficient.
Director
Joined: 12 Nov 2016
Posts: 790
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

27 Sep 2017, 06:53
Manbehindthecurtain wrote:
Are x and y both positive?

(1) $$2x-2y = 1$$

(2) $$\frac{x}{y} > 1$$

Statement 1

2(x-y) =1 - all we know is that the difference of x and y must be positive

too many possibilities- [-4,-5], ; [1/4 , (-1/4)] ; [5, 4] ; [0 (-1/2)]

insuff

Statement 2

Could be negative-negative or positive-positive

insuff

Statement 1 and 2

Using both statements we can rule out the possibility of x being 0 and y being negative and we can rule out the possibility of y being a smaller negative number than x... so the only viable options are positive and positive

C
Intern
Joined: 21 Mar 2017
Posts: 15
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Oct 2017, 06:41
Hi,
What if we consider x=0 and y=-1/2. Then both the conditions are satisfied. So the answer will be e I guess. Please let me know where am I going wrong

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 43892
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Oct 2017, 07:00
Abantika wrote:
Hi,
What if we consider x=0 and y=-1/2. Then both the conditions are satisfied. So the answer will be e I guess. Please let me know where am I going wrong

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app

How is x/y > 1 satisfied if x = 0 and y = -1/2?
_________________
Intern
Joined: 21 Mar 2017
Posts: 15
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

22 Oct 2017, 07:28
OK.I was actually interpreting it as x>y. thanks

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app
Intern
Joined: 26 Feb 2017
Posts: 22
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

04 Dec 2017, 22:39
Bunuel wrote:
zerotoinfinite2006 wrote:
Manbehindthecurtain wrote:
Are x and Y both positive?

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

I guessed and got it right with a 50/50 guess at the end.

What I have done here is this

1) 2x - 2y = 1
hence x - y = \frac{1}{2} {Dividing both side by 2}
In sufficient

2) x > y Alone in sufficient

When (1) + (2) We can say that if X is greater than y than x-y will yield a positive result.

Please correct me if I am wrong

First of all: the question is "are x and Y both positive?" not whether "x-y will yield a positive result".

Next, the red part is not correct.

$$\frac{x}{y}>1$$ does not mean that $$x>y$$. If both $$x$$ and $$y$$ are positive, then $$x>y$$, BUT if both are negative, then $$x<y$$. What you are actually doing when writing $$x>y$$ from $$\frac{x}{y}>1$$ is multiplying both parts of inequality by $$y$$: never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero.

So from (2) $$\frac{x}{y}>1$$, we can only deduce that $$x$$ and $$y$$ have the same sigh (either both positive or both negative).

See the complete solution of this problem in my previous post.

Hope it helps.

Need urgent help on this one.Please my exam is tomorrow.

(1) + (2) means x-y = 0.5 and x>y ; cant we take example of x = -3 and y = -3.5 and solve
Math Expert
Joined: 02 Sep 2009
Posts: 43892
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

### Show Tags

04 Dec 2017, 22:45
kartzcool wrote:
Need urgent help on this one.Please my exam is tomorrow.

(1) + (2) means x-y = 0.5 and x>y ; cant we take example of x = -3 and y = -3.5 and solve

x/y > 1 doe NOT mean that x > y. This is explained several times on previous pages.

Next, it's not clear what you mean by "solve".

Please read the whole discussion. There are a lot of useful information.
_________________
Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1   [#permalink] 04 Dec 2017, 22:45

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

Display posts from previous: Sort by

# Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.