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

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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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.
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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22 Jan 2017, 12:50
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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
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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...
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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 ??
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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

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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.
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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.

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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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.
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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.
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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.

But my question is , how do you get 1/y from (x-y)/y ?
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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30 Jul 2017, 10:30
pclawong wrote:

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.
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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.
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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

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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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?
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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

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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1 [#permalink]

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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.
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Re: Are x and y both positive? (1) 2x-2y = 1 (2) x/y > 1   [#permalink] 04 Dec 2017, 22:45

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