Analytical Problem 5

The planning committee of an academic conference is planning a series of panels using eight professors, M, N, Q, R, S, T, U, and V. Each panel must be put together in accordance with the following conditions:

N, T, and U cannot all appear on the same panel.

M. N, and R cannot all appear on the same panel.

Q and V cannot appear on the same panel.

If V appears on a panel, at least two professors of the trio M, S, and U must also appear on the panel.

Neither R nor Q can appear on a panel unless the other also appears on the panel.

If S appears on a panel, both N and V must also appear on that panel.

Question I

Which of the following CANNOT appear on a panel with R?

(A) M

(B) N

(C) Q

(D) S

(E) T

Question II

Exactly how many of the professors can appear on a panel alone?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Question III

If neither V nor N appears on a panel, then which of the following must be true?

(A) M appears on the panel.

(B) Q appears on the panel.

(C) T appears on the panel.

(D) S does not appear on the panel.

(E) U does not appear on the panel.

Question IV

If S appears on a panel, that panel must consist of at least how many professors?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

Question V

Which of the following is an acceptable group of professors for a panel?

(A) M, N, Q, R

(B) M, Q, R,T

(C) M, R, T, U

(D) M, S, U, V

(E) N,R,T,U

Question VI

Which of the following groups of professors can form an acceptable panel by doing nothing more than adding one more professor to the group?

(A) M, R, T

(B) N,Q,M

(C) Q,R, S

(D) Q,R,V

(E) V, R, N

Question VII

Of the group N, S, T, U, V, which professor will have to be removed to form an acceptable panel?

(A) N

(B) S

(C) T

(D) U

(E) V

Solution for GRE Math Problem 71:

Peter's grade > Victor's grade

Georgette’s grade > Victor's grade

We can’t determine, which of these grades is higher

Answer:D

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