Hey folks,
I've just reviewed Q62 (Data Sufficiency) from the Quant. Review of the OG (2nd ed.).
In doing so I was wondering about the answer explanation for this question. There was one thing I got really stuck with:
Q62:
"In the equation x²+bx+12=0, x is a variable and b is a constant. What is the value of b?"
(1) x-3 is a factor of x²+bx+12.
I fully understood 2 of the possible 3 Methods explained to solve this problem. But I was struggling with this one:
Method 3: The value of b can be found by long division (no issue to understand the long division):
x²+bx+12 : (x-3) = x + (3+b) + (3b+21)/(x-3)
So the remainder is obviously (3b+21).
Then, I have a problem with the following statement in the answer explanation:
"Since the remainder must be 0, it follows that 3b+21=0,or b=-7;SUFFICIENT"
Why is it that the remainder must be 0 ???
Can anyone help?
Kind regards,
Tobi
I've just reviewed Q62 (Data Sufficiency) from the Quant. Review of the OG (2nd ed.).
In doing so I was wondering about the answer explanation for this question. There was one thing I got really stuck with:
Q62:
"In the equation x²+bx+12=0, x is a variable and b is a constant. What is the value of b?"
(1) x-3 is a factor of x²+bx+12.
I fully understood 2 of the possible 3 Methods explained to solve this problem. But I was struggling with this one:
Method 3: The value of b can be found by long division (no issue to understand the long division):
x²+bx+12 : (x-3) = x + (3+b) + (3b+21)/(x-3)
So the remainder is obviously (3b+21).
Then, I have a problem with the following statement in the answer explanation:
"Since the remainder must be 0, it follows that 3b+21=0,or b=-7;SUFFICIENT"
Why is it that the remainder must be 0 ???
Can anyone help?
Kind regards,
Tobi
