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# If x and y are positive, is 4x > 3y? (1) x > y - x (2)

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Manager
Joined: 30 Jan 2006
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If x and y are positive, is 4x > 3y? (1) x > y - x (2) [#permalink]  07 Aug 2007, 12:13
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If x and y are positive, is 4x > 3y?
(1) x > y - x
(2) x/y < 1
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Director
Joined: 12 Jul 2007
Posts: 865
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E for this one.

4x > 3y = x > 3/4y

1. x > y-x

2x > y
x > 1/2y

INSUFFICIENT

2. x/y < 1

x < y

INSUFFICIENT

Together we get 1/2y < x < y

but we can't determine if it's greater than 3/4y
Intern
Joined: 06 Aug 2007
Posts: 38
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I'm voting for C.... :arrow: eek supposed to be E!

1. X>Y-X is 2X>Y, which is INSUFF

2. X/Y<1 is X<Y, which is INSUFF

Considering both, the equation becomes X<Y<2X, which is 3X<3Y<6X

Last edited by Kalyan on 07 Aug 2007, 13:07, edited 2 times in total.
Senior Manager
Joined: 24 Nov 2006
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Re: DS [#permalink]  07 Aug 2007, 12:43
smily_buddy wrote:
If x and y are positive, is 4x > 3y?
(1) x > y - x
(2) x/y < 1

The question says, "is y<4x/3?" We reorder the inequality to make it look like the eq of a line.

(1) y<2x. Let x=3 and y=5; the ineq holds, but y<4x/3 doesn't hold. Let x=3 and y=1; the ineq and the problem's question hold. Therefore, Insuff.

(2) y<x. By simple inspection: y<x<4x/3. This info is sufficient for answering the question and therefore B.
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
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Re: DS [#permalink]  07 Aug 2007, 12:46
smily_buddy wrote:
If x and y are positive, is 4x > 3y?
(1) x > y - x
(2) x/y < 1

(1) x > y - x
2x > y
4x > 2y
6x > 3y. so nsf.

(2) x/y < 1
y > x
3y > 3x
4y > 4x. still nsf.

1 and 2:

6x + 4y > 3y + 4x
2x > - y nsf.........

E.
Senior Manager
Joined: 24 Nov 2006
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fresinha12 wrote:
i dont think we can do the bold...

eschn3am wrote:
E for this one.

4x > 3y = x > 3/4y

1. x > y-x

2x > y
x > 1/2y

INSUFFICIENT

2. x/y < 1

x < y

INSUFFICIENT

Together we get 1/2y < x < y

but we can't determine if it's greater than 3/4y

Of course we can. Dividing/multiplying a positive term (1/2, in this case) doesn't alter the order of the sign nor anything else in the expression.
Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
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Kudos [?]: 181 [0], given: 2

my bad..i thought you were multiplying by 1/x

no clue why i thought thaat....i am getting too tired..grrrr

Andr359 wrote:
fresinha12 wrote:
i dont think we can do the bold...

eschn3am wrote:
E for this one.

4x > 3y = x > 3/4y

1. x > y-x

2x > y
x > 1/2y

INSUFFICIENT

2. x/y < 1

x < y

INSUFFICIENT

Together we get 1/2y < x < y

but we can't determine if it's greater than 3/4y

Of course we can. Dividing/multiplying a positive term (1/2, in this case) doesn't alter the order of the sign nor anything else in the expression.
Manager
Joined: 22 May 2006
Posts: 184
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: DS [#permalink]  08 Aug 2007, 05:00
Andr359 wrote:
smily_buddy wrote:
If x and y are positive, is 4x > 3y?
(1) x > y - x
(2) x/y < 1

The question says, "is y<4x/3?" We reorder the inequality to make it look like the eq of a line.

(1) y<2x. Let x=3 and y=5; the ineq holds, but y<4x/3 doesn't hold. Let x=3 and y=1; the ineq and the problem's question hold. Therefore, Insuff.

(2) y<x. By simple inspection: y<x<4x/3. This info is sufficient for answering the question and therefore B.

The question says x<y not y<x ! E for me.
Re: DS   [#permalink] 08 Aug 2007, 05:00
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