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01 Mar 2024, 04:55
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Numerator: C
Denominator: A+B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (02:34) correct
56%
(02:39)
wrong
based on 988
sessions
History
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Result
Not Attempted Yet
There are exactly three steps—Steps 1, 2, and 3, in that order—used to assemble light bulbs at a particular factory. Some of the bulbs fail to make it through every step in the assembly process; if a bulb fails a given step, it will not proceed to the next step. For the most recent month, the factory manager knows the number of bulbs that were started as well as each of the following:
A = the number of bulbs making it through Step 1 only;
B = the number of bulbs making it through at least Step 2;
C = the number of bulbs making it through all three steps.
The manager wishes to know the fraction of the bulbs that made it through Step 1 that also made it through all three steps. In the table, choose for Numerator and Denominator the expressions that will give the factory owner the fraction desired. Make only two selections, one in each column.
A = the number of bulbs making it through Step 1 only;
B = the number of bulbs making it through at least Step 2;
C = the number of bulbs making it through all three steps.
The manager wishes to know the fraction of the bulbs that made it through Step 1 that also made it through all three steps. In the table, choose for Numerator and Denominator the expressions that will give the factory owner the fraction desired. Make only two selections, one in each column.
ID: 700176
| Numerator | Denominator | |
| A | ||
| B | ||
| C | ||
| A+B | ||
| A-C | ||
| B+C |
ShowHide Answer
Official Answer
Numerator: C
Denominator: A+B
16 Sep 2024, 10:18
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1. Draw out the process described in the problem.
2. Mark on the diagram what the manager wants us to find. D and N are the denominator and numerator, respectively.
3. Note the known number of bulbs for the most recent month (A,B,C).
4. Looking at the previous 2 diagrams, notice that N = C and D = A + B. So, the answer is \(\frac{C}{A+B}\).
Image_1.jpeg [ 27.18 KiB | Viewed 7973 times ]
Image_2.jpeg [ 29.86 KiB | Viewed 7948 times ]
Image_3.jpeg [ 29.17 KiB | Viewed 7957 times ]
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2. Mark on the diagram what the manager wants us to find. D and N are the denominator and numerator, respectively.
3. Note the known number of bulbs for the most recent month (A,B,C).
4. Looking at the previous 2 diagrams, notice that N = C and D = A + B. So, the answer is \(\frac{C}{A+B}\).
Attachment:
Image_1.jpeg [ 27.18 KiB | Viewed 7973 times ]
Attachment:
Image_2.jpeg [ 29.86 KiB | Viewed 7948 times ]
Attachment:
Image_3.jpeg [ 29.17 KiB | Viewed 7957 times ]
Attachment:
Image_4.jpeg [ 35.46 KiB | Viewed 7927 times ]
09 Mar 2024, 21:08
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parkhydel
A - the number of bulbs that made it through Step 1 ONLY. So they made it through Step 1 but not through Step 2. So they failed at step 2 so were discarded. Say there were 100 of these.
B - The number of bulbs that made it through at least Step 2. So they are the ones that succeeded at steps 1 and 2 both. What happened at step 3, we don't know. Say there were 500 of these.
This means that 100 + 500 = 600 bulbs came out of Step 1 but 100 were discarded at Step 2 while 500 succeeded at Step 2. This is the most important point in this question.
C - The ones that made it through all 3 steps. Some part of the 500 that succeeded at step 3 too. Say 450.
The fraction of the bulbs that made it through Step 1 that also made it through all three steps = 450/600
Hence, ANSWER will be \(\frac{C}{(A+B)}\)
