This is a Data Sufficiency question. Let's analyze both statements separately and together to determine whether we can find the exact number of employees in the company.
Let the number of employees in the company be E.
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Statement (1):
"If 5 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company."
Mathematically, this means:
E + 5 ≥ 20
E ≥ 15
This tells us that the number of employees is at least 15, but it does not give an exact value for E. So, this statement alone is insufficient.
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Statement (2):
"If no additional employees are hired by the company and 5 of the present employees resign, there will be fewer than 13 employees in the company."
Mathematically, this means:
E - 5 < 13
E < 18
This tells us that the number of employees is less than 18, but it does not give an exact value for E. So, this statement alone is insufficient.
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Combining Both Statements:
From Statement (1):
E ≥ 15
From Statement (2):
E < 18
Combining both inequalities:
15 ≤ E < 18
So, E can be 15, 16, or 17. Since we do not have a unique value for E, the information is still insufficient.
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Final Answer:
(E) The statements together are still insufficient.