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# Are x and y both positive?

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Manager
Joined: 11 Jan 2006
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Location: Arkansas, US
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Re: Are x and y both positive? [#permalink]

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05 Oct 2006, 21:53
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...
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ARISE AWAKE AND REST NOT UNTIL THE GOAL IS ACHIEVED

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

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06 Oct 2006, 14:10
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
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Location: Arkansas, US
WE 1: 2.5 yrs in manufacturing
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Re: Are x and y both positive? [#permalink]

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07 Oct 2006, 18:54
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...
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Re: Are x and y both positive? [#permalink]

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25 Jun 2014, 20:20
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.
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Re: Are x and y both positive? [#permalink]

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25 Jun 2014, 21:50
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....
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Re: Are x and y both positive? [#permalink]

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26 Jun 2014, 01:07
Expert's post
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
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Re: Are x and y both positive?   [#permalink] 26 Jun 2014, 01:07

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