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
or
. 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
, and the answer to the question posed is "no." Or,
Case II: Group B has some other items at high and low
prices, so
. 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
, or it could be wildly expensive, so that
. We still have insufficient information to answer
the question.
The correct answer is (E).
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