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
The juice stall at the circus stocked just 2 brands of
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Let n=50, implying that 50% of the sold juice packs are A, while the other half are B.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)
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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$${\text{Particular}}\,\,{\text{case}}\,\,:\,\,n = 100\,\,\, \Rightarrow \,\,\,{\text{only}}\,\,A\,\,{\text{sold}}\,\,\,\, \Rightarrow m = 100\,\,\,\left( {{\text{target}}\,\,{\text{value}}} \right)$$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
$$\left( A \right)\,\,\frac{{100 \cdot 100}}{{150 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( B \right)\,\,\frac{{200 \cdot 100}}{{250 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( C \right)\,\,\frac{{200 \cdot 100}}{{300 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{Yes}}!\,\,\,\, \Rightarrow \,\,\,\,{\text{survivor}}!$$
$$\left( D \right)\,\,\frac{{250 \cdot 100}}{{400 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$\left( E \right)\,\,\frac{{300 \cdot 100}}{{500 - 100}}\,\,\mathop = \limits^? \,\,100\,\,\,\,{\text{No}}!$$
$$?\,\,:\,\,\left( C \right)\,\,\,,\,\,\,{\text{only}}\,\,{\text{survivor}}$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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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: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
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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