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16 Aug 2024, 06:07
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P: 1
Q: 4
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (02:39) correct
17%
(02:52)
wrong
based on 1312
sessions
History
Date
Time
Result
Not Attempted Yet
After a 16-member team at Company A saw a certain software demonstration, each of the team members gave the software exactly one of the ratings 1, 2, 3, 4, or 5, where greater numbers indicate higher ratings. The team's manager intended to record the 16 ratings but accidentally recorded one team member's rating twice. The ratings she recorded show two ratings of 1, two ratings of 2, two ratings of 3, two ratings of 4, and nine ratings of 5, for a total of 17 ratings. The manager determined that the extra rating was ____P____, and after this extra rating was removed, the average (arithmetic mean) of the remaining 16 ratings was exactly ____Q____.
Select for P and for Q the options that create a statement that is consistent with the information provided. Make only two selections, one in each column.
Select for P and for Q the options that create a statement that is consistent with the information provided. Make only two selections, one in each column.
ID: 700356
| P | Q | |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 |
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Official Answer
P: 1
Q: 4
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22 Aug 2024, 05:59
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After the extra rating was removed, there were 16 ratings.
Looking at the answer choices, we see that they are all integers: 1, 2, 3, 4, and 5.
So, since average = sum/number, the sum of all the ratings must be a multiple of 16 so that sum/16 = an integer.
Adding all 17 ratings, we get 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + (5 × 9) = 65
If we remove one 1, the sum becomes 64, which equals 16 × 4.
If we remove any other of the 17 ratings we get the following:
65 - 2 = 63 not a multiple of 16
65 - 3 = 62 not a multiple of 16
65 - 4 = 61 not a multiplel of 16
65 - 5 = 60 not a multiple of 16
So, the only way to get a sum of the ratings that is a multiple of 16 is to remove one 1.
Thus, the correct answer for P is 1, and the correct answer for Q is 64/16 = 4.
Looking at the answer choices, we see that they are all integers: 1, 2, 3, 4, and 5.
So, since average = sum/number, the sum of all the ratings must be a multiple of 16 so that sum/16 = an integer.
Adding all 17 ratings, we get 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + (5 × 9) = 65
If we remove one 1, the sum becomes 64, which equals 16 × 4.
If we remove any other of the 17 ratings we get the following:
65 - 2 = 63 not a multiple of 16
65 - 3 = 62 not a multiple of 16
65 - 4 = 61 not a multiplel of 16
65 - 5 = 60 not a multiple of 16
So, the only way to get a sum of the ratings that is a multiple of 16 is to remove one 1.
Thus, the correct answer for P is 1, and the correct answer for Q is 64/16 = 4.
General Discussion
21 Oct 2024, 10:34
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1. We are given a set of 17 ratings and need to find the extra rating - P - and the average of the remaining 16 ratings - Q.
2. It is known that \(Q = \frac{sum - P}{16} = \frac{2 * 1 + 2 * 2 + 2 * 3 + 2 * 4 + 9 * 5 - P}{16} = \frac{65 - P}{16}= \frac{64 + 1 - P}{16} = 4 + \frac{1-P}{16}\).
3. If P is 2, 3, 4, or 5 then Q won't be a whole number. So, P = 1.
4. Then, \(Q = 4 + \frac{1 - 1}{16} = 4\).
5. So, our answer will be P = 1 and Q = 4.
2. It is known that \(Q = \frac{sum - P}{16} = \frac{2 * 1 + 2 * 2 + 2 * 3 + 2 * 4 + 9 * 5 - P}{16} = \frac{65 - P}{16}= \frac{64 + 1 - P}{16} = 4 + \frac{1-P}{16}\).
3. If P is 2, 3, 4, or 5 then Q won't be a whole number. So, P = 1.
4. Then, \(Q = 4 + \frac{1 - 1}{16} = 4\).
5. So, our answer will be P = 1 and Q = 4.
