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The juice stall at the circus stocked just 2 brands of

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The juice stall at the circus stocked just 2 brands of

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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)

OA C

Source: Princeton Review

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BTGmoderatorDC wrote:
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)
Let n=50, implying that 50% of the sold juice packs are A, while the other half are B.
In other words, the store sells an EQUAL NUMBER of each type of juice pack.

Let the store sell 2 OF EACH TYPE of juice pack.
Revenue from two $1 packs of A = 2*1 = 2.
Revenue from two $1.5 packs of B = 2*1.5= 3.
m = revenue percentage from A = (revenue from A)/(total revenue) = 2/(2+3) = 2/5 = 40%.

Since the question stem asks for the value of m, the correct answer must yield a value of 40 when n=50.

Only C works:
(200n)/(300-n) = (200*50)/(300-50) = (200*50)/(250) = 200/5 = 40.

The correct answer is C.

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BTGmoderatorDC wrote:
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)
Source: Princeton Review
$${\text{Particular}}\,\,{\text{case}}\,\,:\,\,n = 100\,\,\, \Rightarrow \,\,\,{\text{only}}\,\,A\,\,{\text{sold}}\,\,\,\, \Rightarrow m = 100\,\,\,\left( {{\text{target}}\,\,{\text{value}}} \right)$$

$$\left( A \right)\,\,\frac{{100 \cdot 100}}{{150 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( B \right)\,\,\frac{{200 \cdot 100}}{{250 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( C \right)\,\,\frac{{200 \cdot 100}}{{300 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{Yes}}!\,\,\,\, \Rightarrow \,\,\,\,{\text{survivor}}!$$
$$\left( D \right)\,\,\frac{{250 \cdot 100}}{{400 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( E \right)\,\,\frac{{300 \cdot 100}}{{500 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$

$$?\,\,:\,\,\left( C \right)\,\,\,,\,\,\,{\text{only}}\,\,{\text{survivor}}$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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BTGmoderatorDC wrote:
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)

OA C

Source: Princeton Review
Let’s let p = the total number of juice tetra packs. Since brand A accounts for n% (or n/100) of the sales of the juice tetra packs, brand B accounts for (100-n)% (or (100 - n)/100) of the the sales of the juice tetra packs. Therefore, we have:

Sales of Brand A juice / total sales = fraction of stall revenue from Brand A sales

[1 x n/100 x p] / [1 x n/100 x p + 1.5 x (100-n)/100 x p] = m/100

[1 x n/100] / [1 x n/100 + 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

Alternate Solution:

Let 100 be the total number of juice tetra packs. Thus, n packs of brand A and (100 - n) packs of brand B were sold. Since brand A accounted for m% (or m/100) of the total revenue, we can create the equation:

(1 x n)/[1 x n + 1.5 x (100 - n)] = m/100

n/(n + 150 - 1.5n) = m/100

n/(150 - 0.5n) = m/100

Multiplying the left hand side by 2/2, we have:

2n/(300 - n) = m/100

200n/(300 - n) = m

Answer: C

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