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

[bhumika.k.shah]

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]

[kunal_kc]

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

[bhumika.k.shah]

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????

[kunal_kc]

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.

[thephoenix]

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

[bhumika.k.shah]

o ok!
but can u explain by pluggin #s???

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

[bhumika.k.shah]

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....

[bigmonkey31]

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.

[bhumika.k.shah]

Wow ! thats some heavy dose of math for me !!!

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.

[thephoenix]

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....