The Juice Stall at the Circus Stocked just 2 brands of Orange Juice GMAT Problem Solving

Question: The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to m% of stall’s revenue and accounted for n% of sales of juice tetra packs. Which of the following expresses m in terms of n?

(A) 100n/(150 – n)
(B) 200n/(250-n)
(C) 200n/(300-n)
(D) 250n/(400-n)
(E) 300n/(500-n)

Correct Answer: C
Solution and Explanation:
Approach Solution 1:

You must use the information provided in the question to solve this GMAT problem-solving question. The issues in this category come from a variety of mathematical disciplines. Particularly, this one comes from circles.
The choice is presented in a way that makes it challenging to choose the right response. The candidates must understand the proper strategy to obtain the needed response. Out of the five options provided, only one is accurate.

Given in the question that There were just 2 types of orange juice tetra packs available at the circus juice stand. Brand B costs $1.5 for each pack whereas Brand A just costs $1. Brand A was responsible for n% of sales of juice tetra packs last week and contributed m% of the stall's earnings. It has asked to find out which of the following defines m as the product of n and m.

Let's say 100 units were sold. Then (100-n) units of B and n units of A are sold.

Total revenue equals the sum of the revenue owed to A and B.
= (Number of Units Sold * Cost Per Unit of A) + (Number of Units Sold * Cost Per Unit of B)
= n *1 + (100-n) *1.5
= n + (150-1.5n) — (1)

But as we already know, A's revenue accounts for m% of total revenue (2)
We must relate (1) and (2) in order to represent m in terms of n. 4. m% = n / (n + (150-1.5n)) or m= 100n / 150-0.5n = 200n/ (300-n)

C is the correct answer.

Approach Solution 2:

You must use the information provided in the question to solve this GMAT problem-solving question. The issues in this category come from a variety of mathematical disciplines. Particularly, this one comes from circles.
The choice is presented in a way that makes it challenging to choose the right response. The candidates must understand the proper strategy to obtain the needed response. Out of the five options provided, only one is accurate.

As stated in the question, there were just 2 types of orange juice tetra packs available at the circus juice stand. Brand B costs $1.5 for each pack whereas Brand A just costs $1. Brand A was responsible for n% of sales of juice tetra packs last week and contributed m% of the stall's earnings. It has asked to find out which of the following defines m as the product of n and m.

Let p equal the overall quantity of juice tetra packs. Brand B accounts for (100-n)% (or (100 - n)/100) of the sales of juice tetra packs because brand A only accounts for n% (or n/100) of the sales of juice tetra packs. As a result, we have:

Brand sales Juice sales as a percentage of all sales equals Brand's stall revenue. the sales

[1 x n/100 p] / [1 x n/100 p + 1.5 x (100-n)/100 p] = m/100
1 x n/100 divided by 1 x n/100 plus 1.5 x (100-n)/100 = m/100
(n/100)/[n/100 + 1.5(100-n)/100] = m/100
n/[n + 1.5(100 - n)] = m/100
100n/[n + 150 - 1.5n] = m
100n/[150 - 0.5n] = m
200n/[300 - n] = m

C is the correct answer.

Approach Solution 3:

1. Let the number of units sold be 100. Then n units of A are sold and (100 - n) units of B are sold
   Total revenue = Revenue due to A + Revenue due to B
   = (No. of units of A sold * cost/unit of A) + (No. of units of B sold * cost/unit of B)
   = n * 1 + (100 - n) * 1.5
   = n + (150 - 1.5n) — (1)
2. But, we know, revenue due to A = m% of the total revenue — (2)
3. To express m in terms of n we need to relate (1) and (2)
4. m% = n / (n + (150 - 1.5n))
   Or m = 100n / 150 - 0.5n = 200n / (300 - n)

C is the correct answer

“The juice stall at the circus stocked just 2 brands of orange" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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