x and y are consecutive positive integers and x>y. X^2

x and y are consecutive positive integers and x>y. X^2 -

Oldest

Best Reply

Author

Message

TAGS:

CEO

Joined: 21 Jan 2007

Posts: 2797

Location: New York City

Followers: 5

Kudos [?]: 132 [0], given: 4

x and y are consecutive positive integers and x>y. X^2 - [#permalink]

06 Nov 2007, 22:49

x and y are consecutive positive integers and x>y.

X^2 - 1 > Y^2 - 4y + x - 1

Which represents all the possible values of Y?

y>=0
y>0
y>1
y>7
y>8

CEO

Joined: 21 Jan 2007

Posts: 2797

Location: New York City

Followers: 5

Kudos [?]: 132 [0], given: 4

Re: inequalities [#permalink]

06 Nov 2007, 23:01

bmwhype2 wrote:

x and y are consecutive positive integers and x>y

X^2 - 1 > Y^2 - 4y + x - 1

Which represents all the possible values of Y?

y>=0
y>0
y>1
y>7
y>8

simplifying the equation we get
X(x+1) > y(y+4)
(y+1) (y+1-1)> y(y-4)
y+1 > y-4
1 > 4

can someone elaborate on why y+1 > y-4 becomes 1 > 4?????

SVP

Joined: 01 May 2006

Posts: 1837

Followers: 8

Kudos [?]: 71 [0], given: 0

Re: inequalities [#permalink]

07 Nov 2007, 00:15

bmwhype2 wrote:

x and y are consecutive positive integers and x>y

X^2 - 1 > Y^2 - 4y + x - 1

Which represents all the possible values of Y?

y>=0
y>0
y>1
y>7
y>8

simplifying the equation we get
X(x+1) > y(y+4)
(y+1) (y+1-1)> y(y-4)
y+1 > y-4
1 > 4

can someone elaborate on why y+1 > y-4 becomes 1 > 4?????

We have 1 > -4 not 1 > 4.... That means it's always true for y > 0

CEO

Joined: 29 Aug 2007

Posts: 2530

Followers: 41

Kudos [?]: 357 [0], given: 19

Re: inequalities [#permalink]

07 Nov 2007, 01:34

bmwhype2 wrote:

x and y are consecutive positive integers and x>y

X^2 - 1 > Y^2 - 4y + x - 1

Which represents all the possible values of Y?

y>=0
y>0
y>1
y>7
y>8

simplifying the equation we get
X(x+1) > y(y+4)
(y+1) (y+1-1)> y(y-4)
y+1 > y-4
1 > 4

can someone elaborate on why y+1 > y-4 becomes 1 > 4?????

x^2 - 1 > y^2 - 4y + x - 1
x^2 - x > y^2 - 4y
x (x-1) > y (y-4)
(y+1) (y+1-1)> y(y-4)
y(y+1) > y(y-4)
y(y+1) - y(y-4) > 0
y (y+1-y+4) > 0
y (y+1-y+4) > 0
y (5) > 0
y > 0

Current Student

Joined: 28 Dec 2004

Posts: 3440

Location: New York City

Schools: Wharton'11 HBS'12

Followers: 11

Kudos [?]: 134 [0], given: 2

[#permalink]

07 Nov 2007, 08:11

I agree y>0

try any value of y..i.e 1/2 /1/4..5 it holds

SVP

Joined: 28 Dec 2005

Posts: 1612

Followers: 1

Kudos [?]: 53 [0], given: 2

[#permalink]

02 Dec 2007, 16:04

i get until x(x-1) > y(y-4) .... how do you get to the next step ?

Senior Manager

Joined: 06 Aug 2007

Posts: 371

Followers: 1

Kudos [?]: 19 [0], given: 0

[#permalink]

02 Dec 2007, 18:31

pmenon wrote:

i get until x(x-1) > y(y-4) .... how do you get to the next step ?

pmenon..since x>y and they are consecutive so x = y + 1.

SVP

Joined: 01 May 2006

Posts: 1837

Followers: 8

Kudos [?]: 71 [0], given: 0

Re: inequalities [#permalink]

03 Dec 2007, 00:00

bmwhype2 wrote:

Fig wrote:

bmwhype2 wrote:

x and y are consecutive positive integers and x>y

X^2 - 1 > Y^2 - 4y + x - 1

Which represents all the possible values of Y?

y>=0
y>0
y>1
y>7
y>8

simplifying the equation we get
X(x+1) > y(y+4)
(y+1) (y+1-1)> y(y-4)
y+1 > y-4
1 > 4

can someone elaborate on why y+1 > y-4 becomes 1 > 4?????

We have 1 > -4 not 1 > 4.... That means it's always true for y > 0

why?

Because:
o The domain of definition for y is "all positive integers"... So y > 0
o 1 > -4 remains valid all time... So on the domain of definition for y.

Manager

Joined: 03 Sep 2006

Posts: 237

Followers: 1

Kudos [?]: 5 [0], given: 0

[#permalink]

03 Dec 2007, 00:36

Ans B (the same method as GMAT TIGER)

SVP

Joined: 28 Dec 2005

Posts: 1612

Followers: 1

Kudos [?]: 53 [0], given: 2

[#permalink]

15 Dec 2007, 12:16

wow, forgot about this question and the fact that I had actually tried it.

Ended up with B. woo hoo

[#permalink] 15 Dec 2007, 12:16

		Similar topics	Author	Replies	Last post
Similar Topics:		If x=3y, is x^2>y^2? 1). y+x<y*x 2). x^2=9y^2	iced_tea	4	08 Oct 2006, 23:14
		x and y are consecutive positive integers and x>y x^2	Hermione	5	24 Nov 2006, 23:28
		Is X^3>y^2 1) y=x^2 2) x>x^2	dimitri92	1	23 May 2010, 00:33
	8	For positive integers x and y, x^2 = 350y. Is y divisible	jayaddula	12	09 May 2012, 16:25
	1	Are the positive integers x and y consecutive?	daviesj	3	06 Jan 2013, 08:04

x and y are consecutive positive integers and x>y. X^2 -

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

x and y are consecutive positive integers and x>y. X^2 -

x and y are consecutive positive integers and x>y. X^2 -

Main navigation

GMAT Resources

Partners

MBA Resources