Bunuel wrote:
If a and b are integers, and b > 0, does \(\frac{a - 1}{b + 1} = \frac{a}{b}\) ?
(1) a = b − 4
(2) a = –b
Given: a and b are integers, and b > 0 Target question: Does (a - 1)/(b + 1) = a/b?This is a good candidate for
rephrasing the target question. Take the equation:
(a - 1)/(b + 1) = a/bCross multiply to get:
(b)(a - 1) = (a)(b + 1)Expand both sides to get:
ab - b = ab + aSubtract ab from both sides to get:
-b = aAdd b to both sides to get:
0 = a + bREPHRASED target question: Does a +b = 0?Aside: The video below has tips on rephrasing the target question Statement 1: a = b − 4 Let's TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = -2 and b = 2. In this case, a + b = (-2) + 2 = 0. So, the answer to the target question is
YES, a+b = 0Case b: a = -1 and b = 3. In this case, a + b = (-1) + 3 = 2. So, the answer to the target question is
NO, a+b does NOT equal 0Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a = –bAdd b to both sides to get:
a + b = 0The answer to the target question is
YES, a+b = 0Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
RELATED VIDEO