M06-25

Question

If there are 78 people working at an office, how many of them are women who are 40 or older?

(1) The number of men working at the office is twice that of women.
 
(2) The number of men and women under the age of 40 is equal.

Bunuel · Answer

Official Solution:

If there are 78 people working at an office, how many of them are women who are 40 or older? 
 
(1) The number of men working at the office is twice that of women.
 
This statement implies there are 26 women and 52 men in the office. However, we don't have information about their respective ages. Not sufficient.
 
(2) The number of men and women under the age of 40 is equal.
 
This statement implies that the number of younger men equals the number of younger women, but we still don't know the exact count of women who are 40 or older. Not sufficient.
 
(1)+(2) Combining both statements, we understand that there are 26 women in total and an equal number of younger men and younger women. But without knowing the exact count of younger women, we cannot determine how many of the 26 women are 40 or older. Not sufficient.

Answer: E

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

gmatchile1 · Answer

To solve this question, we need to evaluate the sufficiency of each statement individually and then consider them together if necessary.
(1) Statement Alone: This statement tells us that the number of men is twice the number of women at the office. However, it does not provide any information about the age distribution of the employees. Therefore, statement (1) alone is not sufficient to answer the question.

(2) Statement Alone: This statement informs us that the number of men and women under the age of 40 is equal. Again, this statement does not provide any information about the number of women older than 40. Thus, statement (2) alone is not sufficient to answer the question.

Considering Both Statements Together: Combining the information from both statements, we know that there are twice as many men as women and that the number of men and women under 40 is equal. However, this still does not give us enough information to determine the number of women older than 40. Therefore, both statements together are not sufficient to answer the question.

Hence, the correct answer is Option E: Statements (1) and (2) TOGETHER are NOT sufficient.

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M06-25

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