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04 Feb 2024, 11:17
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
63% (02:46) correct
37%
(02:40)
wrong
based on 564
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At a certain library, 1600 books were checked out by patrons yesterday. If each patron checked out at least 1 book and at most 10 books yesterday, was the number of patrons who checked out books yesterday greater than 300?
(1) 80 patrons checked out 1 or 2 books each.
(2) 150 patrons checked out 3 or 4 books each.
(1) 80 patrons checked out 1 or 2 books each.
(2) 150 patrons checked out 3 or 4 books each.
04 Feb 2024, 17:01
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At a certain library, 1600 books were checked out by patrons yesterday. If each patron checked out at least 1 book and at most 10 books yesterday, was the number of patrons who checked out books yesterday greater than 300?
This is a max/min question. To evaluate whether the statements provide sufficient information, we'll seek to determine whether we can use the maximum or minimum possible number of patrons indicated by the statements to determine whether the number of patrons who checked out books yesterday was greater than 300.
This kind of question isn't super hard, but we'll be making multiple calculations for each statement. So, we have to be careful to execute well so that we don't arrive at an incorrect answer.
(1) 80 patrons checked out 1 or 2 books each.
Max:
To find the maximum number of patrons indicated by this statement, we'll minimize the number of books checked out by each patron.
80 patrons × 1 book = 80 books
1520 books left --> 1 book per patron --> 1520 more patrons
No more work necessary since the max is over 1520 and thus must be over 300.
Min:
To find the minimum number of patrons indicated by this statement, we'll maximize the number of books checked out by each patron.
80 patrons × 2 books = 160 books
1440 books left --> 10 books per patron --> 144 more patrons
Min = 80 + 144 = 224 patrons
The maximum indicated by this choice is over 1520, and the mininum is 224. So, given what this choice says, the number could be greater or less than 300.
Insufficient.
(2) 150 patrons checked out 3 or 4 books each.
Max:
To find the maximum number of patrons indicated by this statement, we'll minimize the number of books checked out by each patron.
150 patrons × 3 books = 450 books
1150 books left --> 1 book per patron --> 1150 more patrons
No more work necessary since the max is over 1150 and thus must be over 300.
Min:
To find the minimum number of patrons indicated by this statement, we'll maximize the number of books checked out by each patron.
150 patrons × 4 books = 600 books
1000 books left --> 10 books per patron --> 100 more patrons
Min = 150 + 100 = 250 patrons
The maximum indicated by this choice is over 1150, and the mininum is 250. So, given what this choice says, the number could be greater or less than 300.
Insufficient.
Statements (1) and (2) combined
Max:
To find the maximum number of patrons indicated by the statements combined, we'll minimize the number of books checked out by each patron.
Notice that, since we'll have 80 patrons who checked out 1 book and 150 who checked out 3, this number will be the same as the max for Statement (2), which we arrived at by having 150 patrons check out 3 books and the rest check out 1.
Thus, the maximum for the statements combined is over 1150.
Min:
To find the minimum number of patrons indicated by the statements combined, we'll maximize the number of books checked out by each patron.
80 patrons × 2 books = 160 books
150 patrons × 4 books = 600 books
840 books left --> 10 books per patron --> 84 more patrons
Min = 80 + 150 + 84 = 314 patrons
The maximum indicated by this choice is over 1150, and the mininum is 314. So, given what this choice says, the number must be greater than 300.
Sufficient.
Correct answer:
This is a max/min question. To evaluate whether the statements provide sufficient information, we'll seek to determine whether we can use the maximum or minimum possible number of patrons indicated by the statements to determine whether the number of patrons who checked out books yesterday was greater than 300.
This kind of question isn't super hard, but we'll be making multiple calculations for each statement. So, we have to be careful to execute well so that we don't arrive at an incorrect answer.
(1) 80 patrons checked out 1 or 2 books each.
Max:
To find the maximum number of patrons indicated by this statement, we'll minimize the number of books checked out by each patron.
80 patrons × 1 book = 80 books
1520 books left --> 1 book per patron --> 1520 more patrons
No more work necessary since the max is over 1520 and thus must be over 300.
Min:
To find the minimum number of patrons indicated by this statement, we'll maximize the number of books checked out by each patron.
80 patrons × 2 books = 160 books
1440 books left --> 10 books per patron --> 144 more patrons
Min = 80 + 144 = 224 patrons
The maximum indicated by this choice is over 1520, and the mininum is 224. So, given what this choice says, the number could be greater or less than 300.
Insufficient.
(2) 150 patrons checked out 3 or 4 books each.
Max:
To find the maximum number of patrons indicated by this statement, we'll minimize the number of books checked out by each patron.
150 patrons × 3 books = 450 books
1150 books left --> 1 book per patron --> 1150 more patrons
No more work necessary since the max is over 1150 and thus must be over 300.
Min:
To find the minimum number of patrons indicated by this statement, we'll maximize the number of books checked out by each patron.
150 patrons × 4 books = 600 books
1000 books left --> 10 books per patron --> 100 more patrons
Min = 150 + 100 = 250 patrons
The maximum indicated by this choice is over 1150, and the mininum is 250. So, given what this choice says, the number could be greater or less than 300.
Insufficient.
Statements (1) and (2) combined
Max:
To find the maximum number of patrons indicated by the statements combined, we'll minimize the number of books checked out by each patron.
Notice that, since we'll have 80 patrons who checked out 1 book and 150 who checked out 3, this number will be the same as the max for Statement (2), which we arrived at by having 150 patrons check out 3 books and the rest check out 1.
Thus, the maximum for the statements combined is over 1150.
Min:
To find the minimum number of patrons indicated by the statements combined, we'll maximize the number of books checked out by each patron.
80 patrons × 2 books = 160 books
150 patrons × 4 books = 600 books
840 books left --> 10 books per patron --> 84 more patrons
Min = 80 + 150 + 84 = 314 patrons
The maximum indicated by this choice is over 1150, and the mininum is 314. So, given what this choice says, the number must be greater than 300.
Sufficient.
Correct answer:
19 Aug 2024, 14:43
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mmdfl
At a certain library, 1600 books were checked out by patrons yesterday. If each patron checked out at least 1 book and at most 10 books yesterday, was the number of patrons who checked out books yesterday greater than 300?
(1) 80 patrons checked out 1 or 2 books each.
(2) 150 patrons checked out 3 or 4 books each.
An alternate approach is to test the threshold: to test whether it's possible for exactly 300 patrons to check out 1600 books.(1) 80 patrons checked out 1 or 2 books each.
(2) 150 patrons checked out 3 or 4 books each.
Statement 1:
80 patrons, 1 or 2 books each --> 80 to 160 books
220 patrons, 3 to 10 books each --> 660 to 2200 books
Combining the two ranges, we get:
Total checked out --> 1460 to 2360 books ---> 300 patrons can check out 1600 books
Clearly, the number of patrons could just as easily be 301.
Since the answer is NO in the first case but YES in the second, INSUFFICIENT.
Statement 2:
150 patrons, 3 or 4 books each --> 450 to 600 books
150 patrons, a minimum of 1 and a maximum of 10 books each --> 150 to 1500 books
Combining the two ranges, we get:
Total checked out --> 600 to 2100 books ---> 300 patrons can check out 1600 books
Clearly, the number of patrons could just as easily be 301.
Since the answer is NO in the first case but YES in the second, INSUFFICIENT.
Statements combined:
80 patrons, 1 or 2 books each --> 80 to 160 books
150 patrons, 3 or 4 books each --> 450 to 600 books
70 patrons, 5 to 10 books each --> 350 to 700 books
Combining the three ranges, we get:
Total checked out --> 880 to 1460 books ---> 300 patrons are too few to check out 1600 books
Implication:
The number of patrons must exceed 300, with the result that the answer to the question stem is YES.
SUFFICIENT.
