Which one of the following could be an accurate list of the paintings bought by the museum and the private collector,...

Victoria on September 17, 2020

Hi @ivandaquial,

Happy to help!

We know that six paintings are sold at auction: Q, R, S, T, V, and Z.

Three are sold to a museum and three are sold to a private collector.

Two of the paintings are from the artist's first period (1), two are from her second period (2), and two are from her third period (3).

The private collector and the museum each buy one painting from each period.

M: _ _ _
1 2 3

P: _ _ _
1 2 3

Now let's go through the conditions.

Rule 1 - S, which is sold to P, is from an earlier period than Z, which is sold to M.

S > Z

This means that S is not from the third period and Z is not from the first period. The order could be:

1) S1Z2
2) S1Z3
3) S2Z3

Rule 2 - Q is not from an earlier period than T

T > Q

We can make similar deductions to above; however, we don't know who buys these paintings:

1) T1Q2
2) T1Q3
3) T2Q3

However, there is also one more deduction we can make. We know that Q is not from an earlier period than T, but this does not necessarily mean that T is from an earlier period than Q. T and Q could be from the same period (T = Q).

Rule 3 - V is from the artist's second period.

V = 2

Overall Setup:

M: _ _ _ Z
1 2 3

P: _ _ _ S
1 2 3

S > Z

T > Q or T = Q

V = 2

The question stem asks us to select the answer choice which could be an accurate list of the paintings bought by each party, listed in order of period from 1 to 3. Therefore, we are looking for the answer choice which could be true. The incorrect answer choices cannot be true.

We can eliminate answer choice (A) because it violates Rule 2. In this list, Q is from the first period and T is from the third period, but we know that Q is not from an earlier period than T.

We can eliminate answer choice (C) because it violates Rule 1 as S is sold to the museum.

We can eliminate answer choice (D) for violating Rule 3. We know that V is from the second period, but it is from the third period in this list.

Finally, we can eliminate answer choice (E) because it violates Rule 1. We know that S is from an earlier period than Z. In this list, they are both from the artist's first period.

This means that answer choice (B) should be our correct answer, but let's double check.

M: R Z Q
1 2 3

P: S V T
1 2 3

Notice that this meets all of our conditions:

1) S is sold to P. Z is sold to M. S is from an earlier period (1) than Z (2).
2) Q (3) is not from an earlier period than T (3).
3) V is from the second period.

Hope this helps! Please let us know if you have any further questions.