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Question of the Week  43 (While working individually, each of A, B)
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Updated on: 18 Apr 2019, 02:19
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eGMAT Question of the Week #43While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following can be the time they will take to produce 60 units, if all are working together? A. 28.2 minutes B. 46.75 minutes C. 60 minutes D. 63.15 minutes E. 79 minutes
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Originally posted by EgmatQuantExpert on 12 Apr 2019, 03:56.
Last edited by chetan2u on 18 Apr 2019, 02:19, edited 1 time in total.
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Re: Question of the Week  43 (While working individually, each of A, B)
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12 Apr 2019, 05:12
EgmatQuantExpert wrote: eGMAT Question of the Week #43While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time they will take to produce 60 units, if all are working together? A. 28.2 minutes B. 46.75 minutes C. 60 minutes D. 63.15 minutes E. 79 minutes so a, b, c and d can be written as a, a+1, a+2 and a+3... If A and C together can produce 60 units in more than 2 hours...\(\frac{1}{a}+\frac{1}{c}<\frac{1}{2}\)... Just substitute a.. a as 1.. c is 3.. \(1+(\frac{1}{3})=\frac{4}{3} >\frac{1}{2}\) a as 3.. c is 5...\((\frac{1}{3})+(\frac{1}{5})=\frac{8}{15}>\frac{1}{2}\) So, minimum value of a is 4.. Thus the least time all four will take is if a, b, c, and d are 4, 5, 6 and 7... \(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}=\frac{5*6*7+4*6*7+4*5*7+4*5*6}{4*5*6*7}=\frac{210+168+140+120}{840}=\frac{638}{840}.......\).. so time = 840/638 hrs = \(\frac{840*60}{638}\) minutes = 78.99 minutes.. So, the least value is 78.99.. Thus all choices A to D are not possible.. E EgmatQuantExpert, please relook what are you looking for.. which of the following cannot or can be the time they will take to produce 60 units
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Re: Question of the Week  43 (While working individually, each of A, B)
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12 Apr 2019, 05:52
chetan2u wrote: EgmatQuantExpert wrote: eGMAT Question of the Week #43While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time they will take to produce 60 units, if all are working together? A. 28.2 minutes B. 46.75 minutes C. 60 minutes D. 63.15 minutes E. 79 minutes so a, b, c and d can be written as a, a+1, a+2 and a+3... If A and C together can produce 60 units in more than 2 hours...\(\frac{1}{a}+\frac{1}{c}<\frac{1}{2}\)... Just substitute a.. a as 1.. c is 3.. \(1+(\frac{1}{3})=\frac{4}{3} >\frac{1}{2}\) a as 3.. c is 5...\((\frac{1}{3})+(\frac{1}{5})=\frac{8}{15}>\frac{1}{2}\) So, minimum value of a is 4.. Thus the least time all four will take is if a, b, c, and d are 4, 5, 6 and 7... \(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}=\frac{5*6*7+4*6*7+4*5*7+4*5*6}{4*5*6*7}=\frac{210+168+140+120}{840}=\frac{638}{840}.......\).. so time = 840/638 hrs = \(\frac{840*60}{638}\) minutes = 78.99 minutes.. So, the least value is 78.99.. Thus all choices A to D are not possible.. E EgmatQuantExpert, please relook what are you looking for.. which of the following cannot or can be the time they will take to produce 60 units Is there a typo in the question? It says which of the following "cannot" be the time taken. Posted from my mobile device



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Re: Question of the Week  43 (While working individually, each of A, B)
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12 Apr 2019, 10:35
given a,b,c,d are consective integers so a=x ,b=x+1, c= x+2, d= x+3 also given 1/a + 1/c>1/2 use hit and trial to see at which value of x we get 1/a + 1/c>1/2 only at a=4 and c=6 we get >1/2 so a=4,b=5,c=6,d=7 working together 1/4+1/5+1/6+1/7 = 5*6*7+4*6*7+4*5*7+4*5*6/ (4*5*6*7 ) solve we get 638/840 ; time 840*60/638 = ~79 mins IMO E EgmatQuantExpert wrote: eGMAT Question of the Week #43While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time they will take to produce 60 units, if all are working together? A. 28.2 minutes B. 46.75 minutes C. 60 minutes D. 63.15 minutes E. 79 minutes
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Re: Question of the Week  43 (While working individually, each of A, B)
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Updated on: 13 Apr 2019, 05:08
a + c > 2 and a<b<c<d, means, a will take at least 4 hours to complete the work in an hour, units of work completed,
for A, 60*1/4 = 15 B, 60*1/5 = 12 C, 60*1/6=10 D, 60*1/7 ~ 8
Total work = 15+12+10+8 = 45 remaining work= 6045= 15 which 4th of total, so would need additional 4th of an hour, i.e. 15mins,
in all the minimum time would be greater than, 60 + 15 = 75, the only answer which is greater than 75, is E
Originally posted by vijay282001 on 12 Apr 2019, 18:56.
Last edited by vijay282001 on 13 Apr 2019, 05:08, edited 1 time in total.



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Re: Question of the Week  43 (While working individually, each of A, B)
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13 Apr 2019, 01:44
EgmatQuantExpert wrote: While working individually, each of A, B, C and D can produce 60 units of a certain item in a, b, c and d hours respectively, where a, b, c, d are consecutive integers in increasing order. If A and C together can produce 60 units in more than 2 hours, then which of the following cannot be the time they will take to produce 60 units, if all are working together? A. 28.2 minutes B. 46.75 minutes C. 60 minutes D. 63.15 minutes E. 79 minutes For work to complete in 2 hours or less, A and C must complete half the work in an hour. The combined rate of work of A and C cannot be greater than 30 units in an hour. B and D will complete more than 30 units/hr. With increasing time, the rate at which they individually complete the work decreases. Let us assume that A completes the work at 15 units/hr. A will take 4 hours (\(\frac{60}{15} = 4\)) Since the time at which they individually complete work is in consecutive order, B will take 5 hours and the work done by A in an hour is \(\frac{60}{5} = 12\) units. C will take 6 hours and the work done by A in an hour is \(\frac{60}{6} = 10\) units. D will take 7 hours and the work done by A in an hour is \(\frac{60}{7} = 8.5\) units. (approximately) In an hour, they will complete a total of \(15 + 12 + 10 + 8.5 = 45.5\) units. Therefore, the time take to complete the work is \(\frac{60}{45.5} = 1.32\) hours (or) 79 minutes(Option E)
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Question of the Week  43 (While working individually, each of A, B)
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18 Apr 2019, 02:17
Because of the structure of the question, we can devise a shortcut to solving this problem – one that takes only a few seconds  by employing a bit of logic: It stands to reason that the minimum time in which A, B, C and D can complete the work must lie between the highest value (E) and the second highest value (D) thus making E the only possible answer. If the minimum time is less (i.e. between any two of the lesser answer choices), all the answer choices which are more than the minimum time become possible. For example, if the minimum time is 50 minutes (i.e. between B and C), that would make C, D and E all possible but the question allows for only one correct answer. If the minimum time was more than 79 minutes (E) then the correct answer would have been "None" which is not among the answer choices. So the correct answer can only be E. This shortcut can be prevented by changing the structure of the question to allow for more than one correct answer (e.g. D and E, A only, E only, all five, etc.).



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Re: Question of the Week  43 (While working individually, each of A, B)
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20 Apr 2019, 21:37
Hi everyone,
I'm a bit confused and I was hoping to get some clarification on this.
I see an answer that states: (1/a + a/c) > 1/2 Why does a has to be at least 4? If a were to be 1, (1/1 + 1/3) is indeed greater than 1/2.
Another answer states the opposite: (1/a + 1/c) < 1/2 In this case, I do understand that a must be at least 4, but why are we posing (1/a + 1/c) less than 1/2 when we know that it takes a+c at least 2 hours to build 60 units?
Thanks so much for helping! Mike




Re: Question of the Week  43 (While working individually, each of A, B)
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