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# Is f < g?

tagged by: Vincen

#### Is f < g?

Is f < g?

(1) f < g + 1
(2) |f|/|g| < 1

The OA is the option E.

The statement (2) is not sufficient? Why not? Experts, may you help me here?

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Vincen wrote:
Is f < g?

(1) f < g + 1
(2) |f|/|g| < 1

The OA is the option E.

The statement (2) is not sufficient? Why not? Experts, may you help me here?
Test easy cases.

Case 1: g = 1 and f = .5; (This satisfies both statements together) .5 is less than 1, so this yields a YES.
Case 2: g = -2 and f = -1.5. (Again, this satisfies both statements together) -1.5 is not less than -2, so this yields a NO.
Together the statements are not sufficient to answer the question. The answer is E

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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.

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