Source: Princeton Review
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?
$$A.\ \frac{100n}{150-n}$$
$$B.\ \frac{200n}{250-n}$$
$$C.\ \frac{200n}{300-n}$$
$$D.\ \frac{250n}{400-n}$$
$$E.\ \frac{300n}{500-n}$$
The OA is C.
The juice stall at the circus stocked just 2 brands of
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Hi All,
You might recognize this as a 'lift' of an Official Guide question. You can find that question - and a discussion of how to solve it - here:
https://www.beatthegmat.com/what-mistak ... 76293.html
GMAT assassins aren't born, they're made,
Rich
You might recognize this as a 'lift' of an Official Guide question. You can find that question - and a discussion of how to solve it - here:
https://www.beatthegmat.com/what-mistak ... 76293.html
GMAT assassins aren't born, they're made,
Rich
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- Jay@ManhattanReview
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Say the total number of packs sold = xBTGmoderatorLU wrote:Source: Princeton Review
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?
$$A.\ \frac{100n}{150-n}$$
$$B.\ \frac{200n}{250-n}$$
$$C.\ \frac{200n}{300-n}$$
$$D.\ \frac{250n}{400-n}$$
$$E.\ \frac{300n}{500-n}$$
The OA is C.
Thus,
the total number of brand A packs sold = nx/100; and
the total number of brand B packs sold = x - nx/100 = (100x - nx)/100 = x(100 - n)/100
Sales revenue from the sale of brand A = nx/100 * 1 = nx/100
Sales revenue from the sale of brand B = x(100 - n)/100 * 1.5 = 3x(100 - n)/200
=> Total sales revenue from the sale of both the brands = [nx/100 + 3x(100 - n)/200]
Since it is given that brand A contributed to m% of stall's revenue, we have
[nx/100] = m% of [nx/100 + 3x(100 - n)/200]
[n/100] = m[n/100 + 3(100 - n)/200]/100; x gets cancelled
n = m[n/100 + 3(100 - n)/200]; 100 gets cancelled
200n = m(2n + 300 - 3n)
m = (200 n)/(300 - n)
The correct answer: C
Hope this helps!
-Jay
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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:BTGmoderatorLU wrote:Source: Princeton Review
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?
$$A.\ \frac{100n}{150-n}$$
$$B.\ \frac{200n}{250-n}$$
$$C.\ \frac{200n}{300-n}$$
$$D.\ \frac{250n}{400-n}$$
$$E.\ \frac{300n}{500-n}$$
The OA is C.
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
Answer: C
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Let´s explore an AGGRESSIVE PARTICULAR CASE:BTGmoderatorLU wrote:Source: Princeton Review
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?
$$A.\ \frac{100n}{150-n} \,\,\,\,\,\,\, B.\ \frac{200n}{250-n} \,\,\,\,\,\,\, C.\ \frac{200n}{300-n} \,\,\,\,\,\,\, D.\ \frac{250n}{400-n} \,\,\,\,\,\,\, E.\ \frac{300n}{500-n}$$
n = 100 : in this case, only brand A was sold, hence all revenue came from brand A and our FOCUS will be (the TARGET) m =100 (of course)!
\[\left. \begin{gathered}
\left( A \right)\,\,\,\frac{{{{10}^4}}}{{50}} \ne 100 \hfill \\
\left( B \right)\,\,\frac{{2 \cdot {{10}^4}}}{{150}} \ne 100 \hfill \\
\left( C \right)\,\,\frac{{2 \cdot {{10}^4}}}{{200}} = 100\,\,\,\,\, \hfill \\
\left( D \right)\,\,\frac{{25 \cdot {{10}^3}}}{{300}} \ne 100 \hfill \\
\left( E \right)\,\,\frac{{3 \cdot {{10}^4}}}{{400}} \ne 100 \hfill \\
\end{gathered} \right\}\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{only}}\,\,{\text{survivor}}\,{\text{!}}} \,\,\,\,\,\,\,\left( C \right)\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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