Target question: Is 0 < a < 1?
Given: a² = b
Statement 1: 0 < b < 1
There are several values of x and y that satisfy this condition. Here are two:
Case a: a = 0.5 and b = 0.25, in which case
it IS true that 0 < a < 1
Case b: a = -0.5 and b = 0.25, in which case
it is NOT true that 0 < a < 1
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: b < a
GIVEN: a² = b. From this, we can conclude that 0
< b
So, if b < a, then
0 < a (i.e., a is positive)
Let's consider two possible ranges for the value of a.
case a:
0 < a < 1 If this is the case, then a² < a
Since we're told that a² = b, then it must be true that b < a
So, case a yields no contradictions. That is, if
0 < a < 1, then a and b meet the given information as well as statement 2.
case b:
1 < a If this is the case, then a < a²
Since we're told that a² = b, then it must be true that
a < b
Hmmm, this contradicts statement 2.
So, it's IMPOSSIBLE for 1 < a, and for a and b to meet the given information as well as statement 2.
So case a is the ONLY POSSIBLE CASE.
In other words,
it must be true that 0 < a < 1
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
