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

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

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

Re: Are x and y both positive? [#permalink]
26 Jun 2014, 00:07

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.