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10 Aug 2023, 05:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
77% (01:40) correct
23%
(01:51)
wrong
based on 780
sessions
History
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Time
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Each dinner at Restaurant X includes a pair of side dishes, which a customer chooses by selecting any one side dish from list A and any one side dish from list B. There are a total of 18 possible pairs of side dishes, and no side dish appears on both lists. If there are fewer side dishes on list A than on list B, how many side dishes are on list B ?
(1) There are a total of 9 side dishes on the two lists.
(2) There are a total of 3 side dishes on list A.
(1) There are a total of 9 side dishes on the two lists.
(2) There are a total of 3 side dishes on list A.
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10 Aug 2023, 12:37
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Bunuel
Number of side dishes in List A = x
Number of sides dishes in List B = y
Quote:
x * y = 18
Possible combinations of (x,y) =
(1,18)
(2,9)
(3,6)
(6,3)
(18,1)
Quote:
We have to remove the possibility of (6,3) and (18,1).
Possible combinations of (x,y) =
(1,18)
(2,9)
(3,6)
(6,3)
(18,1)
Statement 1
(1) There are a total of 9 side dishes on the two lists.
Out of the three possible pairs indicated in green, the only possible pair of (x,y) = (3,6).
Hence, we have a definite answer to the question, and statement 1 alone is sufficient. We can eliminate options B, C, and E.
Statement 2
(2) There are a total of 3 side dishes on list A.
The statement provides us with the value of \(x\).
\(x = 3.\)
Hence, \(y = 6.\)
\((x,y) = (3,6)\).
We have a definite answer to the question, and statement 2 alone is sufficient.
Option D
General Discussion
29 Aug 2023, 10:10
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Bunuel
Since there is no overlap between the two lists, and since we need to select one item from each of the two lists to make a pair of side dishes, we have:
number of pairs = number of items on list A × number of items on list B = a × b
We know that ab = 18 and a < b and need to answer the question:
b = ?
Statement One Alone:
=> There are a total of 9 side dishes on the two lists.
a + b = 9
From the question stem we know that a and b are integers greater than 1 [because there must be more than 1 item on a list so that a customer has a choice], ab = 18, and a < b, so we have only two cases to evaluate:
If a = 2 and b = 9, then a + b ≠ 9, so this is an invalid case.
If a = 3 and b = 6, then a + b = 9, so this is the only valid case, and thus there are 6 side dishes on list B.
Statement one is sufficient. Eliminate answer choices B, C, and E.
Statement Two Alone:
=> There are a total of 3 side dishes on list A.
a = 3
From the question stem, we know that we have only two cases to evaluate:
If a = 2 and b = 9, then a ≠ 3, so this is an invalid case.
If a = 3 and b = 6, then a = 3, so this is the only valid case, and thus there are 6 side dishes on list B.
Statement two is sufficient.
Answer: D
