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15 Aug 2019, 01:51
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:14) correct
25%
(01:36)
wrong
based on 51
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At a store, the range of the prices in Group A of items is a, and the range of prices in Group B of items is b. If each of the items in Group A is also in Group B, is b greater than a?
(1) Group A contains 21 items.
(2) Group B contains 22 items.
(1) Group A contains 21 items.
(2) Group B contains 22 items.
15 Aug 2019, 06:47
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Group B contains Group A, so we're making Group B by adding a few things to Group A. When you add new values to a set, the range can either stay the same, or, if the newly added values are the new largest or smallest values, the range can increase.
While we know, using both statements, that there is only one new value in Group B, we don't know if that's the largest or smallest value in B, so we don't know if the range of B is greater than the range of A, or if the two ranges are equal, and the answer is E.
While we know, using both statements, that there is only one new value in Group B, we don't know if that's the largest or smallest value in B, so we don't know if the range of B is greater than the range of A, or if the two ranges are equal, and the answer is E.
17 Sep 2019, 04:26
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Bunuel
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).
