Last Monday N female executives (Nandgt;1) received M male managers (Mandgt;1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only?(1) M andlt; 11(2) M(M + 2N) = 65a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer?

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(1) M < 11
(2) M(M + 2N) = 65

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
d)
EACH statement ALONE is sufficient to answer the question asked
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed

Correct answer is option 'B'. Can you explain this answer?

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Last Monday N female executives (N>1) received M male managers (M&g...

Statement (1): M < 11
This statement provides information about the maximum number of male managers, which is less than 11. However, it does not provide any information about the number of female executives or the total number of people present at the meeting. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2): M(M + 2N) = 65
This statement provides an equation relating the number of male managers (M), the number of female executives (N), and the total number of shaking hands. However, we still need to determine the values of M and N to calculate the total number of shaking hands or the number of shaking hands among the female executives only. Therefore, statement (2) alone is not sufficient to answer the question.

Now, let's consider both statements together:

From statement (2), we have M(M + 2N) = 65.

Since the total number of shaking hands is the sum of the shaking hands among the female executives and the shaking hands between male managers and female executives, we can express it as follows:
Total shaking hands = Shaking hands among female executives + Shaking hands between male managers and female executives.

The shaking hands among the female executives can be calculated by selecting 2 out of N people, which is given by the combination formula: N(N-1)/2.

The shaking hands between male managers and female executives can be calculated by multiplying the number of male managers (M) by the number of female executives (N).

Therefore, we can write the equation:
M(M + 2N) = N(N-1)/2 + MN

Simplifying this equation, we get:
M² + 2MN = N(N-1)/2 + MN
M² + MN = N(N-1)/2

We can see that we have one equation with two variables, M and N. Without additional information, we cannot determine the values of M and N uniquely. Therefore, statements (1) and (2) together are not sufficient to answer the question.

Hence, the correct answer is (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Answered by Talent Skill Learning · View profile

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Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only?(1) M < 11(2) M(M + 2N) = 65a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer?

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Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only?(1) M < 11(2) M(M + 2N) = 65a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only?(1) M < 11(2) M(M + 2N) = 65a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the number of shaking hands among the female executives only?(1) M < 11(2) M(M + 2N) = 65a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer?.

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