Question

Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000.Whatwasthemedianpriceofthethreehouses?\left(1\right)ThepriceofTo{m}^{\prime }shousewas$110,000.
(2) The price of Jane's house was $120,000.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Let T, J, and S be the purchase prices for Tom’s, Jane’s, and Sue’s new houses. Given that the average purchase price is 120,000, or T + J + S = 3 * 120000, determine the median purchase price.

1. Given T = 110000, the median could be 120,000 (if J = 120000 and S = 130000) or 125,000 (if J= 125000 and S = 125000); NOT sufficient.
2. Given J = 120000, the following two cases include every possibility consistent with T + J + S = 3 + 120000, or T + S = 2 * 120000. (i) T = S = 120000 (ii) One of T or S is less than 120,000 and the other is greater than 120,000. In each case, the median is clearly 120,000; SUFFICIENT.

• The correct answer is B; statement 2 alone is sufficient.