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10 Jun 2021, 21:45
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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:
95%
(hard)
Question Stats:
39% (02:30) correct
61%
(03:04)
wrong
based on 170
sessions
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Three candles which can burn, 60 minutes, 80 minutes and 100 minutes respectively are lit at different times. All the candles are burning simultaneously for 30 minutes, and there is a total of 40 minutes in which exactly one is burning. For how many minutes are exactly two candles burning?
A. 40
B. 45
C. 50
D. 55
E. 60
A. 40
B. 45
C. 50
D. 55
E. 60
12 Jun 2021, 22:53
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Great underrated question....
We have 3 candles that can burn INDIVIDUALLY for a total of ——> 100+ 80 + 60 = 240 minutes.
When any one of the candles is burning individually and NO OTHER candles are burning ——-> that one candle will take away A - number of minutes from the 240 total minutes each candle would burn individually
When EXACTLY 2 candles are burning, we can say that the amount of time that the 2 candles burn together is = B
However, when Exactly 2 candles are burning together, each will individually be taking away minutes from the 240 total———> so for all the B number of minutes that there are exactly 2 candles burning:
(2) * B minutes will be reducing from the 240 total individual minutes of the 3 candles were they to burn separately
Similar logic applies to the case when exactly 3 candles are burning. We can call this amount of time C ————> and during this time of C minute when all 3 candles burn:
(3) * (C) minutes will be reducing from the 240 total individual minutes of the 3 candles were they to burn separately
So the entire 240 total individual minutes is equal to:
240 = A + (2)*(B) + (3)*(C)
We are told that for 40 minutes, exactly 1 of the candles is burning alone ———-> A = 40 minutes
And we are told that for 30 minutes all 3 candles are burning together ———> C = 30 minutes
Plugging these into the equation:
240 = 40 + (2)*(B) + 90
100 = (2)*(B)
B = 55
Answer:
55 minutes exactly 2 candles will be burning.
Posted from my mobile device
We have 3 candles that can burn INDIVIDUALLY for a total of ——> 100+ 80 + 60 = 240 minutes.
When any one of the candles is burning individually and NO OTHER candles are burning ——-> that one candle will take away A - number of minutes from the 240 total minutes each candle would burn individually
When EXACTLY 2 candles are burning, we can say that the amount of time that the 2 candles burn together is = B
However, when Exactly 2 candles are burning together, each will individually be taking away minutes from the 240 total———> so for all the B number of minutes that there are exactly 2 candles burning:
(2) * B minutes will be reducing from the 240 total individual minutes of the 3 candles were they to burn separately
Similar logic applies to the case when exactly 3 candles are burning. We can call this amount of time C ————> and during this time of C minute when all 3 candles burn:
(3) * (C) minutes will be reducing from the 240 total individual minutes of the 3 candles were they to burn separately
So the entire 240 total individual minutes is equal to:
240 = A + (2)*(B) + (3)*(C)
We are told that for 40 minutes, exactly 1 of the candles is burning alone ———-> A = 40 minutes
And we are told that for 30 minutes all 3 candles are burning together ———> C = 30 minutes
Plugging these into the equation:
240 = 40 + (2)*(B) + 90
100 = (2)*(B)
B = 55
Answer:
55 minutes exactly 2 candles will be burning.
Posted from my mobile device
General Discussion
10 Jun 2021, 22:43
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nick1816
considering this set problem of 3 sets of A=60, B=80, and C=100 element we can calculate the A B, A B and CA given ABC=30
now let A B= X
A B=Y nad CA =Z
and here comes the equation (30-X-Y) + (50-X-Z)+(70-Y-Z)=40 and get the answer X+Y+Z=55
which is the answer
