Maths-
General
Easy

Question

fraction numerator a minus b over denominator a end fraction equals c
In the equation above, if a is negative and b is positive, which of the following must be true?

  1. C > 1
  2. C = 1
  3. c = -1
  4. c < -1

The correct answer is: C > 1


    • We have given the equation
    fraction numerator a minus b over denominator a end fraction equals c
    • The equation can be rewritten as 1 minus b over a equals c,
                                             or .1 minus c equals b over a
    • Since a less than 0 and b greater than 0, it follows that b divided by a less than stack 0 with _ below with _ below
    • And as b/a < 0
      • 1-c < 0, or equivalent to c > 1.
      • Option B is incorrect. If c = 1, then a – b = a, or b = 0. But it is given that b > 0, so c = 1 cannot be true.
      • Option C  is incorrect. If c = -1, then a - b = -a, or 2a = b. But this equation contradicts the premise that a < 0 and b > 0, so c = -1 cannot be true.
      •  Option D is incorrect. For example, if c = -2, then a - b = -2a, or 3a = b. But this contradicts the fact that  and  have opposite signs, so c < -1 cannot be true.

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