Remainder

[nycknicks11]

What is remainder when X^2-4x+11 is divided by 3?

1) x+1 is divisible by 3
2) x-2 is divisible by 3


My way:

1) X^2-4x+11=3q
2) subtract 7 both sides. x^2-4x+4=3q-7
3) (x-2)(x-2)=3q-7
4) since x+1 is divisible by 3; x-2 is divisible by 3. Thus remainder is 2.

Can someone confirm.

[Frankenstein]

What is remainder when X^2-4x+11 is divided by 3?

1) x+1 is divisible by 3
2) x-2 is divisible by 3


My way:

1) X^2-4x+11=3q
2) subtract 7 both sides. x^2-4x+4=3q-7
3) (x-2)(x-2)=3q-7
4) since x+1 is divisible by 3; x-2 is divisible by 3. Thus remainder is 2.

Can someone confirm.

Hi,
I dont understand why you are taking x^2-4x+11 as 3q, which means you are taking it to be divisible by 3.
Your understanding seems to be correct except a minor mistake.
x^2-4x+11= (x-2)^2+7
As, you have pointed that (x-2)^2 is divisible by 3 from (1), the remainder is nothing but remainder when 7 is divided by 3, which gives remainder as 1.

Cheers!

[Anurag@Gurome]

What is remainder when X^2-4x+11 is divided by 3?

1) x+1 is divisible by 3
2) x-2 is divisible by 3


My way:

1) X^2-4x+11=3q
2) subtract 7 both sides. x^2-4x+4=3q-7
3) (x-2)(x-2)=3q-7
4) since x+1 is divisible by 3; x-2 is divisible by 3. Thus remainder is 2.

Can someone confirm.

Solution:
First consider (1) alone.
x^2 - 4x + 11 = (x+1)(x-5) + 16.
Note that x+1 is divisible by 3.
So, the remainder is the remainder obtained when 16 is divided by 3 which is 1.
Or (1) alone is sufficient.
Next consider (2) alone.
X^2 - 4x + 11 = (x-2)^2 - 4 + 11 = (x-2)^2 + 7.
It is given that (x-2) is divisible by 3.
So the remainder is the remainder obtained when 7 is divided by 3 which is 1.
Or, (2) alone is sufficient.

The correct answer is (D).

[nycknicks11]

oops. I meant 3q+R. r= remainder.

Hey anurag, i plugged in 1 for the equation. I got 8 which has a remainder of 2.

[Frankenstein]

oops. I meant 3q+R. r= remainder.

Hey anurag, i plugged in 1 for the equation. I got 8 which has a remainder of 2.

Hi,
If you have plugged in 1, then x+1=2 which is not divisible by 3(contradicts statement1). So, you cannot plug in such values.
Cheers!

[GMATGuruNY]

What is remainder when X^2-4x+11 is divided by 3?

1) x+1 is divisible by 3
2) x-2 is divisible by 3


My way:

1) X^2-4x+11=3q
2) subtract 7 both sides. x^2-4x+4=3q-7
3) (x-2)(x-2)=3q-7
4) since x+1 is divisible by 3; x-2 is divisible by 3. Thus remainder is 2.

Can someone confirm.

For many test-takers, plugging in values would be the most efficient approach.

Statement 1: x+1 is divisible by 3.
x = 2,5,8,11...
When x=2, x²-4x+11 = 7. 7/3 = 2 R1.
When x=5, x²-4x+11 = 16. 16/3 = 5 R1.
When x=8, x²-4x+11 = 43. 43/3 = 14 R1.
When x=11, x²-4x+11 = 88. 88/3 = 29 R1.
R=1 in every case.
Sufficient.

Statement 1: x-2 is divisible by 3.
x = 2,5,8,11...
Same list that we saw in statement 1.
Sufficient.

The correct answer is D.