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

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BSchool Forum Moderator
Joined: 23 May 2018
Posts: 289
Location: Pakistan
GMAT 1: 770 Q48 V50
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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 Sep 2018, 01:48
Manbehindthecurtain wrote:
Are x and y both positive?

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

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

(1) $$2x - 2y = 1$$
$$2(x - y) = 1$$
$$x - y = \frac{1}{2}$$
$$x = y + \frac{1}{2}$$

INSUFFICIENT

(2) $$\frac{x}{y} > 1$$
Only thing we know is that x and y are either both positive or both negative.

INSUFFICIENT

Together

$$\frac{x}{y} > 1$$
$$1 + \frac{y}{2} > 1$$
$$\frac{y}{2} > 0$$

Thus, y is greater than 0 and as x is greater than y, we know that both 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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29 Nov 2018, 22:23
1
Manbehindthecurtain wrote:
Are x and y both positive?

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

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

Quote:
If we are given a statement x/y>1, and we are asked is x and y both positive: is my below mentioned approach correct or is there some gap in my understanding, please help!.

x/y >1
Multiplying above equation by by y^2 both side-------------------------->we can write it as xy>y^2
Therefore,
y(x-y)>0
y(y-x)<0 (sign flips on converting x-y to y-x)
so we have 2 points on number line now 0 and x. hence, y lies between 0 and x --->(0<y<x)
this gives us both x and y are more than zero.
hence, x n y are both positive.

Interesting manipulations! But here is the problem: y lies between 0 and x --->(0<y<x)

y lies between 0 and x does not translate to 0 < y < x.
What if x is negative? Then x < y < 0
Say if x is -3, y will be between -3 and 0.

SO both could be positive BUT both could be negative too.
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Karishma
Veritas Prep GMAT Instructor

Re: Are x and y both positive? (1) 2x - 2y = 1 (2) x/y > 1 &nbs [#permalink] 29 Nov 2018, 22:23

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