How many positive integer values of x less than 10 would satisfy the

Question

How many positive integer values of x less than 10 would satisfy the following inequality  \frac{x^2 - x - 42}{x - 3}\geq{0}   ?

(A) Two
(B) Three
(C) Four
(D) Five
(E) Six

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Kinshook · Answer

Asked: How many positive integer values of x less than 10 would satisfy the following inequality  \frac{x^2 - x - 42}{x - 3}\geq{0}   ?

\frac{x^2 - x - 42}{x - 3}\geq{0} = \frac{(x-7)(x+6)}{x - 3}\geq{0}

x \geq 7  or  -6\leq x \lt 3

x = {1,2,7,8,9} : 5 values

IMO D

keith19 · Answer

Can anyone please explain why 0 is not considered in answer set since the question says >= 0 ?

Bunuel · Answer

Because zero is neither positive nor negative (the only one of this kind).

ZERO:

1. Zero is an  INTEGER .

2. Zero is an  EVEN  integer.

3. Zero is  neither positive nor negative  (the only one of this kind)

4. Zero is  divisible by EVERY integer except 0 itself  ( \frac{0}{x} = 0 , so 0 is a divisible by every number, x).

5. Zero is a  multiple of EVERY integer  ( x*0 = 0 , so 0 is a multiple of any number, x)

6. Zero is  NOT a prime number  (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed:  anything/0 is undefined .

8. Any non-zero number  to the power of 0 equals 1  ( x^0 = 1 )

9.  0^0  case is  NOT tested on the GMAT .

10. If the exponent n is positive (n > 0),  0^n = 0 .

11. If the exponent n is negative (n < 0),  0^n  is undefined, because  0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0} , which is undefined.  You CANNOT take 0 to the negative power .

12.  0! = 1! = 1 .

Hope it helps.

How many positive integer values of x less than 10 would satisfy the

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How many positive integer values of x less than 10 would satisfy the

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