Sofia is in charge of ordering ingredients for a restaurant

Question

Sofia is in charge of ordering ingredients for a restaurant. Only one of the meals on the restaurant's menu features shrimp, and each time that meal is ordered, the restaurant uses exactly 5 shrimp. Sofia will purchase shrimp at a price of 12.50 euros per kilogram, with approximately 42 shrimp per kilogram on average. Sofia determined that if a total of n shrimp meals are ordered at the restaurant per day on average, then a good approximation for the average daily cost to the restaurant, in euros, for the shrimp served can be found by multiplying n by p and dividing the result by q.

Select a value for p and a value for g that would together create the closest approximation from among the options given for the average daily cost, in euros, to the restaurant for the shrimp served. Make only two selections, one in each column.

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Official Answer

p: 3 q: 2

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HarshavardhanR · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=82550 ___ Harsha GMAT-Club-Forum-kdbcf5sa.png

chetan2u · Answer

The information that comes out.. 1) Every shrimp meal has 5 shrimps, so n meals would have 5n shrimps. 2) Almost 42 shrimps come in one kg @ Euros 12.5 per kg, so 1 shrimp would come for \frac{12.5}{42} ~ \frac{12.6}{42} = 0.3 ( We are approximating the answer) 3) Thus, 5n will cost 5n*0.3 or 1.5n Look for \frac{p}{q} that gives a value closer to 1.5 \frac{3}{2} = 1.5 , so p=3 and q=2 GMAT-Club-Forum-1v777ger.png

einstein801 · Answer

That's such a bad approximation though. I only approximated at the end to get 25/15 = 5/3. price per shrimp =12.5/42 = 25/84 price per meal = 5* pps = 125/84 125/84 approx = 125/85 = 25/17 = 25/15 = 5/3 Care to help? GMAT-Club-Forum-hi921zan.png

chetan2u · Answer

No, that is not a bad approximation. That is the best you could do as by a simple increase of 0.1 we are getting a multiple of 42. 
Where you approximate does not matter here. But you cannot be changing the values completely. Changing 17 to 15 is not an approximation. You are changing the number by almost 13-14%. While 12.5 to 12.6 is not even 1%.

You could simply find the answer as the calculator is given. 
12.5*5/42 = 62.5/42 = 1.489~ 1.5 =3/2

user1937 · Answer

Why is this question marked as 805+ level? Is there some subtle point that can be missed here?

Bunuel · Answer

The difficulty level of a question on the site, after sufficient attempts, is determined automatically based on various parameters collected from users' attempts via timer, such as the percentage of correct answers and the time taken to answer the question. So, this is a 805+ level question based on our statistics.

MartyMurray · Answer

Sofia is in charge of ordering ingredients for a restaurant. Only one of the meals on the restaurant's menu features shrimp, and each time that meal is ordered, the restaurant uses exactly 5 shrimp. Sofia will purchase shrimp at a price of 12.50 euros per kilogram, with approximately 42 shrimp per kilogram on average. Sofia determined that if a total of n shrimp meals are ordered at the restaurant per day on average, then a good approximation for the average daily cost to the restaurant, in euros, for the shrimp served can be found by multiplying n by p and dividing the result by q.

Select a value for p and a value for g that would together create the closest approximation from among the options given for the average daily cost, in euros, to the restaurant for the shrimp served. Make only two selections, one in each column.

Show Spoiler

Attachment:

GMAT-Club-Forum-eef1m84t.png

Select a value for p and a value for g that would together create the closest approximation from among the options given for the average daily cost, in euros, to the restaurant for the shrimp served. Make only two selections, one in each column.

Since  n  is the number of meals and the daily cost is  \frac{np}{q} ,  \frac{p}{q}  is the cost per meal.

We can quickly determine the cost per meal as follows:

\frac{5	ext{ shrimp}}{42	ext{ shrimp}} × 12.50 = \frac{62.5}{42} ≈ \frac{63}{42} = 1.5

Thus, we need answers for  p  and  q  such that  \frac{p}{q} = 1.5  or very slightly less than  1.5 .

2

3

5

7

8

The answers for  p  and  q  such that  \frac{p}{q}  is as close as possible to  1.5  are  3  and  2 .

\frac{7}{5}  is less than  1.5 , but it's much less than  1.5  than  \frac{62.5}{42}  is.

So,  \frac{3}{2}  is closest to  \frac{62.5}{42} .

Correct answer:    3  ,   2

Hitesh0701 · Answer

Easiest way to tackle these kind of questions:

1 meal = 5 shrimp
1kg = 12.5 Euros
1kg = 42 shrimps
Combine: 42 shrimps = 12.5 Euros

Now n meals are ordered, Hence, total shrimps required: 5n.
Lets calculate total cost of 5n shrimps
42 shrimps = 12.5 Euros
5n shrimps= ???
12.5 Euros*5n shrimps/42 shrimps: 1.488n (Approximate: 1.5)

Now, we need to calculate p*n/q which is equal to 1.5n
Hence, p/q should give me 1.5 
Hence, p=3, and q=2

Hope this helps.

My idea: 
Just followed the text and calculated figures simultaneously.
This will save much of your time.

KarishmaB · Answer

Daily n meals use 5 shrimps each so we need 5n shrimps. This means she needs 5n/42 kgs of shrimp every day. The cost of this will be 12.5 * \frac{5n}{42} = \frac{62.5n}{42} = \frac{3n}{2} approximately. This is the average daily cost of shrimp. So p = 3 (we multiply n by 3) and q = 2 (we divide n by 2) to get the average daily cost of shrimp. Select 3 and 2 Practice applying the same concept in this question now: https://youtu.be/cWysZoTI4n0

sarthak1701 · Answer

Approximation.

1 kg costs $12.5 and roughly equals 42 shrimps.

Each meal requires 5 shrimps and n meals are ordered daily, therefore 5n shrimps are required daily.

We need a dummy value for n in such a way that 5n is as close to 42 as much as possible.

Let n = 8

5n = 40

42 shrimps cost $12.5 so 40 must cost a little less, let's take it as $12.

n * p/q = 12 = 8 * p/q = 12

Now we just need to experiment with the values

If p = 2

Then 16/q = 12

and q is almost 1.33 but this isn't close to any whole number.

If p = 3

Then 12q = 24 and q = 2. Therefore, p = 3 and q = 2.

It also works if you take n = 9 but the calculation isn't that clean.

If 42 shrimps cost $12.5 then 45 must cost a little more, let's take it at $13.

n = 9

5n = 45

Daily cost = $13

n * p/q = 13

9 * p/q = 13

If p = 2

Then 18/q = 13 and q = 18/13 which approximates to 1.5 and not close to any whole number

If p = 3

9*3/q = 13

27/q = 13

q = 27/13 which approximates to 2.1 which is quite close to 2.

p = 3, q = 2

Yet another way is to increase the number of shrimps and cost to more round numbers

If 42 shrimps cost $12.5, how much would 50 cost? 50 is roughly 20% more than 42, so let's increase the cost per kg by 20% as well which equals $15.

Daily cost = 15

n = 10

10 *p/q = 15

p/q = 3/2

p = 3, q = 2

Sofia is in charge of ordering ingredients for a restaurant

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Sofia is in charge of ordering ingredients for a restaurant

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