BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

x > y , x^2-1 > y^2 -4y + x -1

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

x > y , x^2-1 > y^2 -4y + x -1

by bhumika.k.shah » Tue Jan 26, 2010 5:31 am
If x and y are consecutive positive integers, and x > y , x^2-1 > y^2 -4y + x -1

Then which of the following represents all the possible values of y?

A. y>= 0
B. y>0
C. y>1
D. y >7
E. y > 8

OA B

Since x>y and they are consecutive positive integers can i take x=3 and y=2 ?
Also if i do take it then its not coming correct!

Help ! [/spoiler]
Top
Source: — Problem Solving |
User avatar
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Tue Sep 02, 2008 12:33 am
Thanked: 2 times

by kunal_kc » Tue Jan 26, 2010 5:47 am
if you take x=-2 and y=-3, the equation does not satisfy so y has to be greater than = to 0

next if you take x=1 and y=0, still the equation does not satisfy so y has to be grater than 0

try x=2 and y=1, the equation satisfies hence y can be anything greater than 0

so answer is B
Top
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

by bhumika.k.shah » Tue Jan 26, 2010 5:52 am
But why are you even taking -1 or -2 or 0 #s to plug in the first place , when they are already saying that they are consecutive positie integers????
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Tue Sep 02, 2008 12:33 am
Thanked: 2 times

by kunal_kc » Tue Jan 26, 2010 6:15 am
oops, sorry thanks for correcting me. then you can just take from 1,2 but why you couldn't solve using 2,3. it does satisfy the equation.
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Tue Jan 26, 2010 6:21 am
bhumika.k.shah wrote:If x and y are consecutive positive integers, and x > y , x^2-1 > y^2 -4y + x -1

Then which of the following represents all the possible values of y?

A. y>= 0
B. y>0
C. y>1
D. y >7
E. y > 8

OA B

Since x>y and they are consecutive positive integers can i take x=3 and y=2 ?
Also if i do take it then its not coming correct!

Help ! [/spoiler]
x^2-1>y^2-4y+x_1
and x=y+1(bcoz x>y and bth are consecutive int)

x^2-1-y^2+4y-x+1>0
substituting x=y+1
we get 5y>0
hence y>0
and therfore B
Top
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

by bhumika.k.shah » Tue Jan 26, 2010 9:03 am
o ok!
but can u explain by pluggin #s???
thephoenix wrote:
bhumika.k.shah wrote:If x and y are consecutive positive integers, and x > y , x^2-1 > y^2 -4y + x -1

Then which of the following represents all the possible values of y?

A. y>= 0
B. y>0
C. y>1
D. y >7
E. y > 8

OA B

Since x>y and they are consecutive positive integers can i take x=3 and y=2 ?
Also if i do take it then its not coming correct!

Help ! [/spoiler]
x^2-1>y^2-4y+x_1
and x=y+1(bcoz x>y and bth are consecutive int)

x^2-1-y^2+4y-x+1>0
substituting x=y+1
we get 5y>0
hence y>0
and therfore B
Top
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

by bhumika.k.shah » Tue Jan 26, 2010 9:05 am
Also what made u use x=y+1
coz generally when its given they r consecutive positive integers , the first thing that would strike us is taking #s....
Top
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Sat Jan 02, 2010 1:11 am
Thanked: 3 times
GMAT Score:730

by bigmonkey31 » Tue Jan 26, 2010 6:44 pm
You use x=y+1 because it says that x & y are consecutive but x>y...

So for example, let's say that two consecutive integers we choose are 4 and 5. In this scenario, y=4 and x=5 (by the assumptions given), so we can also say that x = 5 = (4+1) = (y+1), thus x=y+1

This is a very important concept to understand especially for more advanced problems in the GMAT. 3 consecutive integers can be thought of as x, (x+1), (x+2)... OR, another way to think about 3 consecutive integers is (x-1), x, (x+1)


With regards to this specific question, you can even simplify the original equation with substitution to get..

(y+1)(y+2) > y(y-4), which is saying that the product of the next 2 larger consecutive integers (of y) is greater than the product of y and a number 4 units smaller. Thus this is true for any number, y, greater than 0.

B.
Top
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

by bhumika.k.shah » Tue Jan 26, 2010 7:13 pm
Wow ! thats some heavy dose of math for me !!! :-(
bigmonkey31 wrote:You use x=y+1 because it says that x & y are consecutive but x>y...

So for example, let's say that two consecutive integers we choose are 4 and 5. In this scenario, y=4 and x=5 (by the assumptions given), so we can also say that x = 5 = (4+1) = (y+1), thus x=y+1

This is a very important concept to understand especially for more advanced problems in the GMAT. 3 consecutive integers can be thought of as x, (x+1), (x+2)... OR, another way to think about 3 consecutive integers is (x-1), x, (x+1)


With regards to this specific question, you can even simplify the original equation with substitution to get..

(y+1)(y+2) > y(y-4), which is saying that the product of the next 2 larger consecutive integers (of y) is greater than the product of y and a number 4 units smaller. Thus this is true for any number, y, greater than 0.

B.
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

by thephoenix » Tue Jan 26, 2010 9:47 pm
bhumika.k.shah wrote:o ok!
but can u explain by pluggin #s???
plugging is time taking job as one has to plug no's for each choices
a)
y=0--->x=1(to satisfy x>y and x,y are consecutive)
check second case
x^2-1 > y^2 -4y + x -1
0>0( not true)

B)
let y=2 ---> x=3-----> satisfy first condition x>y and x and y are consecutive int
put in second case
x^2-1 > y^2 -4y + x -1
8>-6(true)
but to make it sure we need to check by plugging -ve int
y=-3---->x=-2

second case
3>18( which is not true)
hence y>0 must be true

like wise u can plug for others too....
Top
Post new topic Post Reply
• Page 1 of 1