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

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

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]

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Source: Beat The GMAT — Problem Solving | Tue Jan 26, 2010 5:31 am

kunal_kc: 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

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

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????

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kunal_kc: 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.

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

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

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

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

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

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....

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bigmonkey31: 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.

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

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.

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

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....

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