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A vendor sells only Product A, for $6, and Product B, for

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Magoosh GMAT Instructor
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A vendor sells only Product A, for $6, and Product B, for [#permalink]

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New post 01 Oct 2014, 10:54
3
13
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

61% (03:34) correct 39% (03:09) wrong based on 101 sessions

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A vendor sells only Product A, for $6, and Product B, for $21. If Q% of the products sold are Product B, and if T% of the total revenue comes from sales of Product B, find Q in terms of T.

(A) \(1501T - 15T^2\)

(B) \(\frac{15T}{615 - 6T}\)

(C) \(\frac{21T}{621 - 6T}\)

(D) \(\frac{40T}{140 - T}\)

(E) \(\frac{60T}{160 - T}\)


For the OE on this problem, and more practice Word Problems, see:
https://magoosh.com/gmat/2014/gmat-prac ... -problems/

Mike :-)

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A vendor sells only Product A, for $6, and Product B, for [#permalink]

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New post 01 Oct 2014, 19:41
1
....................... Product A .................... Product B ...................

Per Piece cost...... 6 .................................. 21 ....

Sales ................. \(x - \frac{qx}{100}\) ...................... \(\frac{qx}{100}\) ....................... x (Assume-Total sales)

Total Revenue ........\(r - \frac{tr}{100}\) ..................... \(\frac{tr}{100}\) ......................... r (Assume - Total revenue)

Two equations would be setup:

\(21 * \frac{qx}{100} = \frac{tr}{100}\)

\(\frac{r}{x} = \frac{21q}{t}\) .................... (1)

\(6 * (x - \frac{qx}{100}) = r - \frac{tr}{100}\) ......... (2)

Divide the complete equation (2) by x

\(6 * (1 - \frac{q}{100}) = \frac{r}{x} - \frac{tr}{100x}\)

\(6 * (1 - \frac{q}{100}) = \frac{r}{x} * (1 - \frac{t}{100})\) .................. (3)

Placing value of \(\frac{r}{x}\) (from equation 1) in equation (3)

\(6 * (1 - \frac{q}{100}) = \frac{21q}{t} * (1 - \frac{t}{100})\)

40t = 140q - tq

\(q = \frac{40t}{140-t}\)

Answer = D
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Re: A vendor sells only Product A, for $6, and Product B, for [#permalink]

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New post 01 Jun 2016, 05:09
mikemcgarry wrote:
A vendor sells only Product A, for $6, and Product B, for $21. If Q% of the products sold are Product B, and if T% of the total revenue comes from sales of Product B, find Q in terms of T.

(A) \(1501T - 15T^2\)

(B) \(\frac{15T}{615 - 6T}\)

(C) \(\frac{21T}{621 - 6T}\)

(D) \(\frac{40T}{140 - T}\)

(E) \(\frac{60T}{160 - T}\)


For the OE on this problem, and more practice Word Problems, see:
https://magoosh.com/gmat/2014/gmat-prac ... -problems/

Mike :-)

Let toatal number of product A=A and product B=B
total no. of products sold=(A+B)
total revenue= 6A+21B
As per stem
Q%(A+B)=B -------(a)
T%(6A+21B)=21B-------(b)
from(b) we get
6AT+21BT=2100B
B=6AT/(2100-21T)----(c)
from (a)
QA+QB=100B
B=QA/(100-Q)----(d)
equating (c)&(d)
2100Q-21QT=600T-6QT
Q(2100-15T)=600T
Q=600T/(2100-15T)
dividing by 15 to num. & denom.
Q=40T/(140-T)
Ans D
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Re: A vendor sells only Product A, for $6, and Product B, for [#permalink]

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New post 12 Jul 2016, 21:53
1
mikemcgarry wrote:
A vendor sells only Product A, for $6, and Product B, for $21. If Q% of the products sold are Product B, and if T% of the total revenue comes from sales of Product B, find Q in terms of T.

(A) \(1501T - 15T^2\)

(B) \(\frac{15T}{615 - 6T}\)

(C) \(\frac{21T}{621 - 6T}\)

(D) \(\frac{40T}{140 - T}\)

(E) \(\frac{60T}{160 - T}\)


For the OE on this problem, and more practice Word Problems, see:
https://magoosh.com/gmat/2014/gmat-prac ... -problems/

Mike :-)


Quick way to do this one..

Let the total number of products sold be 100..

We will work with ratio of the individual revenues for Product A and Product B

\(\frac{21Q}{6(100-Q)} = \frac{T}{100-T}\)

Answer (D)

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Re: A vendor sells only Product A, for $6, and Product B, for [#permalink]

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New post 08 Jan 2018, 14:06
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Re: A vendor sells only Product A, for $6, and Product B, for   [#permalink] 08 Jan 2018, 14:06
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