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# Are x and y both positive - GMATPrep

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Manager
Joined: 02 Aug 2007
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Schools: Life
Are x and y both positive - GMATPrep [#permalink]

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18 Jan 2009, 19:26
Are x and y both positive?

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

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Manager
Joined: 02 Aug 2007
Posts: 221
Schools: Life
Re: Are x and y both positive - GMATPrep [#permalink]

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18 Jan 2009, 19:47
Intern
Joined: 09 Jan 2009
Posts: 10
Re: Are x and y both positive - GMATPrep [#permalink]

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18 Jan 2009, 19:59
Is it the correct answer ?
Intern
Joined: 09 Jan 2009
Posts: 10
Re: Are x and y both positive - GMATPrep [#permalink]

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18 Jan 2009, 20:07
Sorry...It looks like the correct answer is E.

Explanation :

x-y=1/2
x>y

Now lets say x=4.5 and y=4 ...this gives x-y=1/2 ...Here x and y are positive.

if we say x=-4 and y=-4.5 then x-y=1/2...Here both x and y are negative.

Isn't it ??

What was the answer in Gmat Prep ??
Manager
Joined: 02 Aug 2007
Posts: 221
Schools: Life
Re: Are x and y both positive - GMATPrep [#permalink]

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18 Jan 2009, 20:23
vicky81 wrote:
Sorry...It looks like the correct answer is E.

Explanation :

x-y=1/2
x>y

Now lets say x=4.5 and y=4 ...this gives x-y=1/2 ...Here x and y are positive.

if we say x=-4 and y=-4.5 then x-y=1/2...Here both x and y are negative.

Isn't it ??

What was the answer in Gmat Prep ??

How do you get x>y? We don't know whether x or y are +ve or -ve, which can change the inequality sign.

OA is C
Senior Manager
Joined: 30 Nov 2008
Posts: 479
Schools: Fuqua
Re: Are x and y both positive - GMATPrep [#permalink]

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18 Jan 2009, 20:56
x-ALI-x wrote:
Are x and y both positive?

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

IMO E

Stmt 1 : 2x - 2y = 1 ==> 2(x - y) = 1 ==> x - y = 1/2.

Here are examples for x and y satisfying Stmt 1 equation. hence cannot say whether X > 0 and Y > 0. Insufficent.

(x, y) = (+,+) ==> x = 1, y = 1/2
(x, y) = (+,-) ==> x = 1/2, y = -1
(x, y) = (-,+) ==> x = -1/2, y = 1
(x, y) = (-,-) ==> x = -1/4, y = -3/4

Stmt 2 : x/y > 1 ==> x > y.

Here are examples for x and y satisfying Stmt 2 equation. hence cannot say whether X > 0 and Y > 0. Insufficent.

(x, y) = (+,+) ==> x = 2, y = 1
(x, y) = (+,-) ==> x = 2, y = -1
(x, y) = (-,+) ==> not possible
(x, y) = (-,-) ==> x = -1, y = -2

Now consider both the stmt together. Here we can conclude that X > 0, but Y can be > 0 or not greater than 0. Hence insufficent.
SVP
Joined: 29 Aug 2007
Posts: 2427
Re: Are x and y both positive - GMATPrep [#permalink]

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18 Jan 2009, 21:22
x-ALI-x wrote:
Are x and y both positive?

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

1: x - y = 1/2. insuff.

2: x/y > 1. both are either -ve or +ve. also insuff.

togather: lxl > lyl otherwise x/y cannot be > 1.

with that constraint, if x and y both are -ve, x - y cannot be 1/2.
if both are +ve, then only x - y = 1/2 possible. therefore suff.

Hence C.
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SVP
Joined: 04 May 2006
Posts: 1787
Schools: CBS, Kellogg
Re: Are x and y both positive - GMATPrep [#permalink]

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19 Jan 2009, 02:44
x-ALI-x wrote:
Are x and y both positive?

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

1) x=y+1/2 clearly not suff

2) is the same as:

(x-y)/y >0, so x and y have the same sign, not suff

1 and 2 suff:(x-y)/y = (1/2)/y >0, so y must be positive, x in turn must be positive also. because x and y have the same sign
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Senior Manager
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Posts: 387
Re: Are x and y both positive - GMATPrep [#permalink]

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19 Jan 2009, 03:12
sondenso wrote:
x-ALI-x wrote:
Are x and y both positive?

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

1) x=y+1/2 clearly not suff

2) is the same as:

(x-y)/y >0, so x and y have the same sign, not suff

1 and 2 suff:(x-y)/y = (1/2)/y >0, so y must be positive, x in turn must be positive also. because x and y have the same sign

sondenso can u please explain the step no. 3 i.e combining both the statement 1+2.........
x-y)/y = (1/2)/y >0,

Manager
Joined: 04 Jan 2009
Posts: 229
Re: Are x and y both positive - GMATPrep [#permalink]

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19 Jan 2009, 10:33
GMAT TIGER wrote:
x-ALI-x wrote:
Are x and y both positive?

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

1: x - y = 1/2. insuff.

2: x/y > 1. both are either -ve or +ve. also insuff.

togather: lxl > lyl otherwise x/y cannot be > 1.

with that constraint, if x and y both are -ve, x - y cannot be 1/2.
if both are +ve, then only x - y = 1/2 possible. therefore suff.

Hence C.

I understand your reasoning that both individually are insufficient.
Now,x>y and x=y+0.5
Are both integers? If not, y can be -0.25 and x can be 0.25 and still we satisfy both statements. Or y can be 1 and x will be 1.5. Thus, both together will not be sufficient.
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tusharvk

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Joined: 29 Aug 2007
Posts: 2427
Re: Are x and y both positive - GMATPrep [#permalink]

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19 Jan 2009, 20:18
tusharvk wrote:
GMAT TIGER wrote:
x-ALI-x wrote:
Are x and y both positive?

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

1: x - y = 1/2. insuff.

2: x/y > 1. both are either -ve or +ve. also insuff.

togather: lxl > lyl otherwise x/y cannot be > 1.

with that constraint, if x and y both are -ve, x - y cannot be 1/2.
if both are +ve, then only x - y = 1/2 possible. therefore suff.

Hence C.

I understand your reasoning that both individually are insufficient.
Now,x>y and x=y+0.5
Are both integers? If not, y can be -0.25 and x can be 0.25 and still we satisfy both statements. Or y can be 1 and x will be 1.5. Thus, both together will not be sufficient.

if y can be -0.25 and x can be 0.25, do they satisfy (1) "x - y = 1/2" and (2) "x/y > 1"/
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Intern
Joined: 19 Jan 2009
Posts: 16
Re: Are x and y both positive - GMATPrep [#permalink]

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19 Jan 2009, 22:35
Are x and y both positive?

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

stmt 1: x - y = 1/2 which is insufficient

stmt 2; x/y > 1 which is insufficient

combined :

stmt 1 can be simplifed to x = y + 1/2

now plug in this in stmt 2

( y + 1/2) / y > 1

1 + 1/2y > 1

1/2y > 0
which implies y is positive so is x .

Manager
Joined: 04 Jan 2009
Posts: 229
Re: Are x and y both positive - GMATPrep [#permalink]

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20 Jan 2009, 06:31
[/quote]
I understand your reasoning that both individually are insufficient.
Now,x>y and x=y+0.5
Are both integers? If not, y can be -0.25 and x can be 0.25 and still we satisfy both statements. Or y can be 1 and x will be 1.5. Thus, both together will not be sufficient.[/quote]

if y can be -0.25 and x can be 0.25, do they satisfy (1) "x - y = 1/2" and (2) "x/y > 1"/[/quote]

Yes. got my mistake. I multiplied both sides of x/y>1 by y without knowing if y is negative or positive.
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tusharvk

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Joined: 04 May 2006
Posts: 1787
Schools: CBS, Kellogg
Re: Are x and y both positive - GMATPrep [#permalink]

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20 Jan 2009, 07:03
gurpreet07 wrote:
sondenso can u please explain the step no. 3

combined :

stmt 1 can be simplifed to x = y + 1/2

now plug in this in stmt 2

( y + 1/2) / y > 1

1 + 1/2y > 1

1/2y > 0
which implies y is positive so is x .

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Are x and y both positive - GMATPrep   [#permalink] 20 Jan 2009, 07:03
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# Are x and y both positive - GMATPrep

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