M40-19

Question

During a festive Christmas Eve toy-making competition, Elvin the elf crafted exactly 75 toys, while Nori the elf crafted exactly 60 toys. How long did the toy-making competition last?

(1) During the competition, Nori the elf's average toy crafting rate was 5 toys per hour slower than Elvin the elf's average rate.
 
(2) During the competition, the ratio of Elvin the elf's average toy crafting rate to Nori the elf's average toy crafting rate was 5 to 4.

Bunuel · Answer

Official Solution:

During a festive Christmas Eve toy-making competition, Elvin the elf crafted 75 toys, while Nori the elf crafted 60 toys. How long did the toy-making competition last? 
 
(1) During the competition, Nori the elf's average toy crafting rate was 5 toys per hour slower than Elvin the elf's average rate.
 
Since Elvin crafts 5 more toys per hour than Nori, to account for the difference of 75 - 60 = 15 toys during the competition, they must have worked for 15/5 = 3 hours. Sufficient.
 
(2) During the competition, the ratio of Elvin the elf's average toy crafting rate to Nori the elf's average toy crafting rate was 5 to 4.
 
This only reiterates what we already know from the stem: Elvin crafted 75 toys and Nori crafted 60 toys, which means the ratio of their rates was 75:60 = 5:4. Not sufficient.

Answer: A

jain67 · Answer

Bunuel  How have we arrived at this- they must have worked for 15/5 = 3 hours?

Bunuel · Answer

The difference in their rates is 5 toys per hour, so to reach the difference of 15 toys, they must have worked for 3 hours.

visheshr · Answer

The intuitive explanation by Bunuel is quite good, which can be represented mathematically below as well using (Rate x Time) = WorkDone

We can extend above formula to:

(Difference between Elvin/Nori's rate) x (Time worked by the elfs) = (Difference in Work)

Since we know, (Elvins' Rate - Nori's Rate) =  5 toys/hour  and (Total difference in Work Done) = (75-60) =  15 toys  then,

Using the underlined formula, (Difference between Elvin/Nori's rate) x (Time worked by the elfs) = (Difference in Work), we get
5t = 15
t = 3

Hence Time worked is 3 hours.

Ishannagpal26 · Answer

Nowhere in the question stem was it mentioned that both of them took the same amount of time making their respective number of toys? How do we assume that here, could someone explain if possible? TIA!

Bunuel · Answer

Notice that both the question and the statements mention "during the competition," meaning the number of toys made by the elves, as well as their average crafting rates, were determined over the duration of the competition.

raghavarora089 · Answer

This is a poor question. What if E made 15 toys per hr and N made 10 toys per hour ? This makes the total time as 10 hrs. We need the C option as well to tell us the exact ratio of their rates to determine that E made 25 toys per hr and N made 20 toys per hour to arrive at 6 hrs as total time taken by both of them. Please help me explain this

Bunuel · Answer

We are told that Elvin the elf crafted 75 toys, while Nori the elf crafted 60 toys. If the total time worked was 10 hours, their rates would be 7.5 and 6 toys per hour, respectively, with a difference of 1.5 toys per hour, not 5.

Again, since Elvin crafts 5 more toys per hour than Nori, to make up the difference of 75 - 60 = 15 toys during the competition, they must have worked for 15/5 = 3 hours.

rajanraju25 · Answer

Why cant we calculate the duration by 75/5 or 60/4 i.e the competiion be 15 hours. Hence the final solution being "each shatement is alone sufficient"

Bunuel · Answer

(2) During the competition, the   ratio   of Elvin the elf's average toy crafting rate to Nori the elf's average toy crafting rate was 5 to 4.

This does not mean that Elvin and Nori's rates are exactly 5 and 4, respectively. It means that the  ratio  of their rates is 5 to 4, so the actual rates could be 5 and 4, 10 and 8, and so on.

bb · Answer

If you can't solve it, it does not mean it is a poor question 😇

SKDEV · Answer

HI  Bunuel   bb 
should the question stem include that "both were making toys simultaneously"
coz its a competition I thought Nori goes first, clocks her time then Elvin goes etc. I thought the times need to be added to find total duration of competition

anyways here is how I solved-
assuming competition goes for t hrs,
and E's rate: x+5 toys/hr
N's rate: x toys/hr

so, xt = 60
(x+5)t = 75
we get t = 3 and x = 20

Bunuel · Answer

The question clearly implies that both were making toys simultaneously, as it’s a competition. Most competitions involve participants working at the same time, not sequentially. There’s no indication of sequential work here, so adding their times isn’t logical or supported by the question. The duration refers to the time they worked together, as is typical in competitions.

saibharatmba · Answer

Your point is correct, but the total time the competition would last is 6 hours. E will complete his 75 toys in 5 hours, while N would have made only 50 by then. N will need another 1 hour to finish remaining 10 toys. This is true if the competition is that E needs to complete 75toys and N needs to complete 60 toys. But here in this case, in a given fixed amount of time in a competition E managed 75 toys and N managed 60. What could be the fixed time of the competition? Suddenly, the explanation in the discussion will make sense. 5 extra toys per hour result in fixed time of 3 hours to compensate extra 3X5 = 15 toys.

raghavarora089

This is a poor question. What if E made 15 toys per hr and N made 10 toys per hour ? This makes the total time as 10 hrs. We need the C option as well to tell us the exact ratio of their rates to determine that E made 25 toys per hr and N made 20 toys per hour to arrive at 6 hrs as total time taken by both of them. Please help me explain this

henrychinaski · Answer

Why is knowing the ratio alone not enough to answer the question?

Bunuel · Answer

The ratio alone is not enough because it doesn't provide any new information beyond what's already in the problem stem (75:60 = 5:4). Statement (2) just restates this and doesn't help determine the duration of the competition.

Rashmi96 · Answer

I did not quite understand the solution. isnt the question asking total time and not just the difference in the time of both people

Bunuel · Answer

The question is asking for the total time of the competition.

From Statement (1), Nori's rate is 5 toys per hour slower than Elvin's. Since they worked for the same amount of time, the difference in the number of toys made (15 toys) is due to this rate difference.

Time = Difference in toys / Difference in rates = 15 / 5 = 3 hours.

This is the total time the competition lasted. Please review the discussion above for further clarification.

bondi123 · Answer

I like the solution - it’s helpful.

M40-19

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