The juice stall at the circus stocked just 2 brands of

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

The juice stall at the circus stocked just 2 brands of

by BTGmoderatorDC » Thu Nov 29, 2018 3:34 pm

Timer

00:00

Your Answer

Global Stats

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

Quote

Source: Beat The GMAT — Problem Solving | Thu Nov 29, 2018 3:34 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Thu Nov 29, 2018 3:54 pm

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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Quote

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Fri Nov 30, 2018 5:32 pm

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.

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

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Apr 04, 2019 5:16 pm

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]