In January there was a large drop in the number of new houses sold, because interest rates for mortgages were falling and many consumers were waiting to see how low the rates would go. This large sales drop was accompanied by a sharp rise in the average price of new houses sold. Which of the following, if true, best explains the sharp rise in the average price of new houses? (A) Sales of higher-priced houses were unaffected by the sales drop because their purchasers have fewer constraints limiting the total amount they pay. (B) Labor agreements of builders with construction unions are not due to expire until the next January. (C) The prices of new houses have been rising slowly over the past three years because there is an increasing shortage of housing. (D) There was a greater amount of moderate-priced housing available for resale by owners during January than in the preceding three months. (E) Interest rates for home mortgages are expected to rise sharply later in the year if predictions of increased business activity in general prove to be accurate

(A) Sales of higher-priced houses were unaffected by the sales drop because their purchasers have fewer constraints limiting the total amount they pay.

Explanation:

The question asks us to state which statement would explain the sharp rise in the average price of new homes sold, and the only option that does that is option A. The average price of new homes sold includes both cheap, middle class and expensive homes, and assuming that the sale of both cheap and middle class homes decreased, the average price of new homes sold would increase because the weight of expensive homes is larger.

E.g. 100 houses are sold:

40 cost around $150,000

50 cost around $300,000

10 cost around $1,000,000

average price = $310,000

sales of cheap and middle class homes decreased, so only 70 were sold:

25 cost around $150,000

35 cost around $300,000

10 cost around $1,000,000

average price = $346,429 (represents an 11.75% increase)