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M05-35

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M05-35  [#permalink]

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New post 16 Sep 2014, 00:26
11
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

47% (03:31) correct 53% (03:11) wrong based on 192 sessions

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Three copy machines are making copies of the same document. Copier A makes 12 copies per minute, Copier B makes 7, and Copier C makes 19. It costs 8 cents/copy for Copier A, 5 cents/copy for Copier B, and 11 cents/copy for Copier C. If a separate attendant has to be hired for each copier and be paid $30 per hour (you have to pay $60 if the attendant works for one hour and one minute), which copier alone will be the most efficient choice to make 1,200 copies?

A. Copier A
B. Copier B
C. Copier C
D. A and B
E. A and C

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New post 16 Sep 2014, 00:26
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1
Official Solution:

Three copy machines are making copies of the same document. Copier A makes 12 copies per minute, Copier B makes 7, and Copier C makes 19. It costs 8 cents/copy for Copier A, 5 cents/copy for Copier B, and 11 cents/copy for Copier C. If a separate attendant has to be hired for each copier and be paid $30 per hour (you have to pay $60 if the attendant works for one hour and one minute), which copier alone will be the most efficient choice to make 1,200 copies?

A. Copier A
B. Copier B
C. Copier C
D. A and B
E. A and C


To find the total cost of copying 1,200 pages, we need to know: 1. How long it takes for an attendant to copy 1,200 pages on each copier. 2. How much it costs per job on each of the machines.

Cost of Time:

A \(\frac{1200}{12} = 100\) mins (exact) costs: $60

B \(\frac{1200}{7} = 170\) mins (approx) costs: $90

C \(\frac{1200}{19} = 63\) mins (approx) costs: $60

Price per Job:

A \(1200*$0.08=$96\)

B \(1200*$0.05=$60\)

C \(1200*$0.11=$132\)

Total cost including attendant's pay:

A \(96+60 = 156\)

B \(60+90 = 150\)

C \(132+60 = 192\)

The best choice is Copier B.


Answer: B
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Re: M05-35  [#permalink]

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New post 16 Jan 2015, 12:13
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Hi Bunuel,

In this case...we figured out the costs associated with the individual printers, and that itself took some time. What about options D and E? are there some generalizations regarding the rate of 2 workers together such as: unless the rate of 2 workers together working together is more than double the rate of any of the individuals....they are better off working alone? would this be a fair generalization?

Thanks,
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Re: M05-35  [#permalink]

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New post 21 Aug 2015, 13:01
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amishra1 wrote:
Hi Bunuel,

In this case...we figured out the costs associated with the individual printers, and that itself took some time. What about options D and E? are there some generalizations regarding the rate of 2 workers together such as: unless the rate of 2 workers together working together is more than double the rate of any of the individuals....they are better off working alone? would this be a fair generalization?

Thanks,


You can eliminate D and E immediately because the question asks "which copier alone will be the most efficient choice to make 1,200 copies?"

This problem is not difficult to understand. However, you have to recognize that it will be very time consuming. Depending on where you are at on the test(in terms of the time you have left and your mental state), you might need to make a random guess among A, B, and C to move on.
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Re: M05-35  [#permalink]

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New post 20 Oct 2015, 03:09
Hi Bunnel,

I didnt get how yoy got $90 for 170min? can you please explain me to clear my doubt?
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Re: M05-35  [#permalink]

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New post 12 Nov 2015, 22:41
I don't get why this problem is 95% hard rated. "Alone" eliminates right away D and E. Machine C is way too slow and expensive so choice C out. You can spend a minute and calculate to rule out whether B or A however at short reasoning B looks preferable.

Why? Because it is faster when the time matters - attendat gets paid for the time spent and every additional minute could count. Although B is more costly in terms of $/1 page - in time constraints I would bet on B without calculation and continue.
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Re: M05-35  [#permalink]

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New post 26 May 2016, 02:48
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chaitanyakankanaka wrote:
Hi Bunnel,

I didnt get how yoy got $90 for 170min? can you please explain me to clear my doubt?

chaitanyakankanaka:
Every 60mins the attendant get $30, next min he'll get extra $30 (cost@60mins = $30, cost@61mins = 30 + 30 = $60)

So, 170mins = 60m + 60m + 50m = 30 + 30 + 30 = $90.
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Re: M05-35  [#permalink]

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New post 10 Feb 2017, 04:23
shasadou wrote:
I don't get why this problem is 95% hard rated. "Alone" eliminates right away D and E. Machine C is way too slow and expensive so choice C out. You can spend a minute and calculate to rule out whether B or A however at short reasoning B looks preferable.

Why? Because it is faster when the time matters - attendat gets paid for the time spent and every additional minute could count. Although B is more costly in terms of $/1 page - in time constraints I would bet on B without calculation and continue.


Why is Machine C way too slow ? I think it's the fastest one with 19 copies per minute ...
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Re: M05-35  [#permalink]

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New post 30 Sep 2017, 13:44
1200/19 is approximately 63 not approximately 61. Also, to be more GMAT like, it should be explicitly stated that rate units stay the same the whole time. Other than that, good question and one that really tests how quickly you can do arithmetic.
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Re: M05-35  [#permalink]

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New post 24 Mar 2019, 06:37
Bunuel wrote:
Official Solution:

Three copy machines are making copies of the same document. Copier A makes 12 copies per minute, Copier B makes 7, and Copier C makes 19. It costs 8 cents/copy for Copier A, 5 cents/copy for Copier B, and 11 cents/copy for Copier C. If a separate attendant has to be hired for each copier and be paid $30 per hour (you have to pay $60 if the attendant works for one hour and one minute), which copier alone will be the most efficient choice to make 1,200 copies?

A. Copier A
B. Copier B
C. Copier C
D. A and B
E. A and C


To find the total cost of copying 1,200 pages, we need to know: 1. How long it takes for an attendant to copy 1,200 pages on each copier. 2. How much it costs per job on each of the machines.

Cost of Time:

A \(\frac{1200}{12} = 100\) mins (exact) costs: $60

B \(\frac{1200}{7} = 170\) mins (approx) costs: $90

C \(\frac{1200}{19} = 63\) mins (approx) costs: $60

Price per Job:

A \(1200*$0.08=$96\)

B \(1200*$0.05=$60\)

C \(1200*$0.11=$132\)

Total cost including attendant's pay:

A \(96+60 = 156\)

B \(60+90 = 150\)

C \(132+60 = 192\)

The best choice is Copier B.


Answer: B





Hi Bunuel

How did you calculate for Copier A, how did you calculate cost of time = $60?
Similarly, for Copier B, how did you calculate cost of time = $90?

Kindly please explain??
Thanks


Would really appreciate your help!
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Re: M05-35  [#permalink]

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New post 24 Mar 2019, 07:38
JIAA wrote:
Bunuel wrote:
Official Solution:

Three copy machines are making copies of the same document. Copier A makes 12 copies per minute, Copier B makes 7, and Copier C makes 19. It costs 8 cents/copy for Copier A, 5 cents/copy for Copier B, and 11 cents/copy for Copier C. If a separate attendant has to be hired for each copier and be paid $30 per hour (you have to pay $60 if the attendant works for one hour and one minute), which copier alone will be the most efficient choice to make 1,200 copies?

A. Copier A
B. Copier B
C. Copier C
D. A and B
E. A and C


To find the total cost of copying 1,200 pages, we need to know: 1. How long it takes for an attendant to copy 1,200 pages on each copier. 2. How much it costs per job on each of the machines.

Cost of Time:

A \(\frac{1200}{12} = 100\) mins (exact) costs: $60

B \(\frac{1200}{7} = 170\) mins (approx) costs: $90

C \(\frac{1200}{19} = 63\) mins (approx) costs: $60

Price per Job:

A \(1200*$0.08=$96\)

B \(1200*$0.05=$60\)

C \(1200*$0.11=$132\)

Total cost including attendant's pay:

A \(96+60 = 156\)

B \(60+90 = 150\)

C \(132+60 = 192\)

The best choice is Copier B.


Answer: B





Hi Bunuel

How did you calculate for Copier A, how did you calculate cost of time = $60?
Similarly, for Copier B, how did you calculate cost of time = $90?

Kindly please explain??
Thanks


Would really appreciate your help!


Check here: https://gmatclub.com/forum/three-copy-m ... 60805.html

Hope it helps.
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Re: M05-35  [#permalink]

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New post 22 Sep 2019, 16:50
Bunuel wrote:
Official Solution:

Three copy machines are making copies of the same document. Copier A makes 12 copies per minute, Copier B makes 7, and Copier C makes 19. It costs 8 cents/copy for Copier A, 5 cents/copy for Copier B, and 11 cents/copy for Copier C. If a separate attendant has to be hired for each copier and be paid $30 per hour (you have to pay $60 if the attendant works for one hour and one minute), which copier alone will be the most efficient choice to make 1,200 copies?

A. Copier A
B. Copier B
C. Copier C
D. A and B
E. A and C


To find the total cost of copying 1,200 pages, we need to know: 1. How long it takes for an attendant to copy 1,200 pages on each copier. 2. How much it costs per job on each of the machines.

Cost of Time:

A \(\frac{1200}{12} = 100\) mins (exact) costs: $60

B \(\frac{1200}{7} = 170\) mins (approx) costs: $90

C \(\frac{1200}{19} = 63\) mins (approx) costs: $60

Price per Job:

A \(1200*$0.08=$96\)

B \(1200*$0.05=$60\)

C \(1200*$0.11=$132\)

Total cost including attendant's pay:

A \(96+60 = 156\)

B \(60+90 = 150\)

C \(132+60 = 192\)

The best choice is Copier B.


Answer: B



I did it this way and it took 4 minutes to answer the question, is there a quicker way to get this or is this just a time intensive question?
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M05-35  [#permalink]

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New post 22 Sep 2019, 18:26
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Bunuel wrote:
Three copy machines are making copies of the same document. Copier A makes 12 copies per minute, Copier B makes 7, and Copier C makes 19. It costs 8 cents/copy for Copier A, 5 cents/copy for Copier B, and 11 cents/copy for Copier C. If a separate attendant has to be hired for each copier and be paid $30 per hour (you have to pay $60 if the attendant works for one hour and one minute), which copier alone will be the most efficient choice to make 1,200 copies?

A. Copier A
B. Copier B
C. Copier C
D. A and B
E. A and C


An alternative approach: First of all, let me say that I did not eliminate choices (D) and (E) right away. For all I knew, copiers A and B would complete the job at the same cost, or copiers A and C would, which would make choices (D) and (E) trick answers instead of obvious snares. With that said, I solved this one using the following method, a combination of number sense and logic (my favorite approach to Quant problems):

1) Figure out the cost per minute per copier -
Copier A: 12 copies/minute * 8 cents/copy = 0.96, or 96 cents per minute
Copier B: 7 copies/minute * 5 cents/copy = 0.35, or 35 cents per minute
Copier C: 19 copies/minute * 11 cents/copy = (1.90 + 0.19), or 2.09 per minute

2) Figure out how long the job will take for each copier and convert to attendant hours -
Copier A: 1,200 copies/(12 copies/minute) = 100 minutes, or 2 attendant hours, based on the problem setup
Copier B: 1,200 copies/(7 copies/minute) ~ 171 minutes, or 3 attendant hours
Copier C: 1,200 copies/(19 copies/minute) ~ 63 minutes, or 2 attendant hours

Now, logic took over. Since Copier C had missed the 1-hour mark and had to share 2-hour space with Copier A, it would have to gain back those $30 on Copier A to be more cost-effective. A few factors, when taken together in the following chain of reasoning, allowed me to rule out this possibility:

1) Copier C cost more than $1.00 per minute than Copier A (2.09 versus 0.96, respectively) for 63 minutes: 63 * $1.00 = $63.00 (as an estimate)
2) Copier A took only 37 minutes more than Copier C to complete the job: 37 * 0.96 < 63

Copier A had to be more cost-effective than Copier C, then, even without working out all the numbers. I got rid of choices (C) and (E). Meanwhile, Copier B had hit the 3-hour attendant mark, so it would also have to pull back $30 on Copier A to be more cost-effective. I approached the numbers in a similar manner as before:

1) Copier A cost 96 - 35, or 61 cents more per minute than Copier B for 100 minutes: 100 * 0.61 = $61.00. (This removes the $30 deficit--$61 - $30 = $31--in favor of Copier B.)
2) Copier B took 71 minutes longer to complete the job than Copier A. 71 * 0.35 < 31. (Calculating tenths, or increments of 10 percent, is almost instantaneous, since each tenth simply slides the decimal one place to the left. Thus, 71 * 0.10 = 7.1, and even four of those (0.40) would be less than 31.)

With choices (A) and (D) out of the way, only one choice, the answer, was left. (B) won out.

I am posting this solution in case anyone else takes a similar approach to this problem or other tough problems like it. Do not discount the power of logic.

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Re: M05-35  [#permalink]

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New post 23 Sep 2019, 09:23
I felt "(you have to pay $60 if the attendant works for one hour and one minute),"
was not clear, so what I infer from this is that $30 for 1 hour and $60 for 2 hours.. so how do I infer it's $30 for 3 hrs??
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New post 23 Sep 2019, 09:53
sankarsh wrote:
I felt "(you have to pay $60 if the attendant works for one hour and one minute),"
was not clear, so what I infer from this is that $30 for 1 hour and $60 for 2 hours.. so how do I infer it's $30 for 3 hrs??


sankarsh - Sorry if my explanation was not clear. Your interpretation is correct: it costs $30 per hour per attendant. Bunuel based his solution on this given information in a clear-cut manner. I was merely highlighting the relative differences between/among two or three copiers at a time. Since we know Copier C costs more per minute to run than Copier A, for instance, and since they both require 2 hours of attendant work (since Copier C barely ticked past the 1-hour mark), any advantage Copier C might gain, in terms of cost-efficiency, by completing the job faster must outweigh the "penalty" of the additional $30 that it incurred, despite the fact that Copier A also required 2 attendant hours. As I showed above, the advantage for C does not outweigh the drawback. The comparison between Copier A and Copier B was more straightforward, and the $30 difference between the two comes from B taking 1 attendant hour longer to complete the job.

If you are still confused, I would be happy to discuss the matter further. I am not saying my solution is better than the official one, by any means. I was just pointing out another way to solve the problem, and sometimes I feel it is good for others who may base their Quant approach on a similar balance between intuition and their mathematical knowledge base to see that it is okay to approach problems creatively.

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Re: M05-35  [#permalink]

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New post 12 Oct 2019, 08:12
Bunuel wrote:
Three copy machines are making copies of the same document. Copier A makes 12 copies per minute, Copier B makes 7, and Copier C makes 19. It costs 8 cents/copy for Copier A, 5 cents/copy for Copier B, and 11 cents/copy for Copier C. If a separate attendant has to be hired for each copier and be paid $30 per hour (you have to pay $60 if the attendant works for one hour and one minute), which copier alone will be the most efficient choice to make 1,200 copies?

A. Copier A
B. Copier B
C. Copier C
D. A and B
E. A and C


I just want to emphasize that you cannot eliminate D and E based on the wording "copier alone." Copier alone is the same as saying as that copier working by itself and not with another copier to share the workload. If the question asked, "which copier is the only one that will be the most efficient choice," then this would eliminate D & E. MentorTutoring explains this in his/her alternative approach above as well.
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Re: M05-35   [#permalink] 12 Oct 2019, 08:12
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