At a store, the range of the prices in Group A of items is a, and the

Official Explanation

In this question, we have two Groups of items, and we want to know about the ranges of their prices--that is, the difference between the most expensive item and the least expensive item in each group. Since all of the items in Group A are in Group B, the most expensive and the least expensive item from Group A are in Group B. So the range of the items' prices must be at least as large in Group B as it is in Group A. It could be larger, if Group B contained a price higher than the maximum of Group A and/or a price lower than the minimum of Group A. So there are two possibilities: either b > a or b = a. Having gathered that, we turn to the statements, separately first.

Statement (1) is not incredibly informative, since we don't know how many items are in Group B. We can analyze by cases. Case I: Group B has the same 21 items Group A has. Then the ranges are the same, because the items and prices are the same, and b = a, and the answer to the question posed is "no." Or, Case II: Group B has some other items at high and low prices, so b > a. Both cases are permitted by the data given, and they yield different answers to the question posed, so we cannot answer the question definitively. Statement (1) is insufficient.

Statement (2), when viewed alone, suffers from a similar problem as Statement (1). Based on the statement, we know nothing about Group A. So we can imagine a case in which they both have 22 items and the same range, or Group A has, say, 21 items, and Group B has a bigger range. Insufficient.

When we combine the statements, we are able to rule out the case in which Group A and Group B have the exact same items. Group B has a "bonus" item. That "bonus" item could either be moderately priced, so that b = a, or it could be wildly expensive, so that b > a. We still have insufficient information to answer the question.

The correct answer is (E).