BTGModeratorVI wrote: ↑Sat May 16, 2020 7:32 am
Is y < z ?
(1) y + z = 1
(2) y^2 < z^2
Answer:
C
Source: Kaplan
Target question: Is y < z ?
Statement 1: y + z = 1
Let's TEST some values.
There are several values of y and z that satisfy statement 1. Here are two:
Case a: y = 0 and z = 1. In this case, the answer to the target question is
YES, y is less than z
Case b: y = 1 and z = 0. In this case, the answer to the target question is
NO, y is not less than z
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y² < z²
There are several values of y and z that satisfy statement 2. Here are two:
Case a: y = 0 and z = 1. In this case, the answer to the target question is
YES, y is less than z
Case b: y = 0 and z = -1. In this case, the answer to the target question is
NO, y is not less than z
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 2 tells us that: y² < z²
Subtract z² from both sides of the inequality to get: y² - z² < 0
Factor the left side to get: (y + z)(y - z) < 0
Since statement 1 tells us that y + z = 1, we can replace (y + z) with 1 to get: (1)(y - z) < 0
Simplify: y - z < 0
Add z to both sides to get:
y < z
The answer to the target question is
YES, y is less than z
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
