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Source: — Data Sufficiency |
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by rijul007 » Wed Nov 16, 2011 10:49 am
Statement 1
x* = x
x(x-1) = x
x^2 -2x = 0
x(x-2) = 0
x = 0 or 2
Insufficient

Statement 2
(x-1)* = x-2
(x-1)(x-2) = x-2
(x-1)(x-2)-(x-2) = 0
(x-2)(x-1-1) = 0
(x-2)(x-2) = 0
x = 2

Sufficient

Option B
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by neelgandham » Wed Nov 16, 2011 12:44 pm
For all integers n, n*=n(n-1). What is the value of x* ?
1) x* = x
Implies x * (x-1) = x
Implies x = 0 or x = 2
Implies x* = 0 or x* = 2,
Insufficient!
2) (x-1)* = x-2
Implies (x-1)*(x-2) = (x-2)
Implies x = 2
Implies x* = 2
Sufficient

Option B
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by chufus » Thu Nov 17, 2011 1:06 am
rijul007 wrote:Statement 1
x* = x
x(x-1) = x
x^2 -2x = 0
x(x-2) = 0
x = 0 or 2
Insufficient

Statement 2
(x-1)* = x-2
(x-1)(x-2) = x-2
(x-1)(x-2)-(x-2) = 0
(x-2)(x-1-1) = 0
(x-2)(x-2) = 0
x = 2

Sufficient

Option B
I think the answer shoud be (D). Here is my explanation !

for every integer n , n* = n(n-1)

Statement 1:

x* = x
which implies:
x(x-1)=x
divide by x on both sides:
x-1 = 1

Add 1 to both sides:

x = 2

Sufficient.....

Statement 2:

(x-1)* = x-2

so (x-1)(x-1-1) = x-2
so (x-1)(x-2) = x-2

Divide by (x-1) on both sides

so x-1 = 1

so x = 2

Sufficient...

The correct answer should be (D) , No?
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by ripulgupta » Thu Nov 17, 2011 2:05 am
chufus wrote: I think the answer shoud be (D). Here is my explanation !

for every integer n , n* = n(n-1)

Statement 1:

x* = x
which implies:
x(x-1)=x
divide by x on both sides:
x-1 = 1

Add 1 to both sides:

x = 2

Sufficient.....

Statement 2:

(x-1)* = x-2

so (x-1)(x-1-1) = x-2
so (x-1)(x-2) = x-2

Divide by (x-1) on both sides

so x-1 = 1

so x = 2

Sufficient...

The correct answer should be (D) , No?
In the first statement after reaching x(x-1)=x you are dividing both sides by 'x' this can be done only if 'x' != 0.

x(x-1) = x
x^2 - x = x
x^2 - 2x = 0
x = 2 or x = 0
thus insufficient.
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