Vincen wrote:Is f < g?
(1) f < g + 1
(2) |f|/|g| < 1
We need to determine whether f < g.
Statement One Alone:
f < g + 1
Statement one alone is not sufficient to answer the question. For example, if f = 2 and g = 2, then f IS NOT less than g. However, if f = 1 and g = 2, then f IS less than g.
Statement Two Alone:
|f|/|g| < 1
We can multiply both sides of the inequality by |g| to get:
|f| < |g|
We can also determine that statement two alone is not sufficient to answer the question.
For example, if f = -1 and g = -2, then f IS NOT less than g. However, if f = 1 and g = 2, then f IS less than g.
Statements One and Two Together:
Using the information from statements one and two, we know that f < g + 1 and that |f| < |g|. This is still not enough information to answer the question.
For example, if f = -1 and g = -1.5, then f IS NOT less than g. However, if f = 1 and g = 2, then f IS less than g.
Answer:
E
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