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A hot dog vendor who sells only hot dogs and soft drinks charges $3

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Bunuel
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A hot dog vendor who sells only hot dogs and soft drinks charges $3 [#permalink] New post  07 Jul 2015, 02:47
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78% (01:54) correct 22% (01:48) wrong based on 219 sessions
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A hot dog vendor who sells only hot dogs and soft drinks charges $3 for a hot dog. If the vendor collected $1,000 in total revenue last month, how much does he charge for a soft drink?

(1) The vendor sold twice as many hot dogs as soft drinks last month.
(2) The revenue from hot dog sales last month was 3/4 of the total monthly revenue.


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Re: A hot dog vendor who sells only hot dogs and soft drinks charges $3 [#permalink] New post  07 Jul 2015, 03:33
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Last month revenue: \(3*N_h + P_s*N_s = $1000\)... Equation (i)

Statement (1): \(N_h = 2*N_s\)
\(6*N_s + P_s*N_s = $1000\)
\(N_s*(6+P_s)=$1000\)
Possible solutions:
\(N_s = 50, P_s = 14\)
\(N_s = 10, P_s = 94\)
NOT sufficient

Statement (2):\(3*N_h=3/4*$1000\)
\(N_h = $250\)

From Equation (i), \(P_s*N_s = $1000-$750\)
\(P_s*N_s = $250\)
Possible solutions:
\(N_s = 50, P_s = 5\)
\(N_s = 5, P_s = 50\)
NOT sufficient

Statement (1) & Statement (2) together:
\(P_s*N_s = $250, N_s*(6+P_s)=$1000\)
\(6*N_s = 1000 - 250\)
\(6 *N_s = 750\)
\(N_s = 125\)
\(250/P_s = 125\)
\(P_s = 2\)

Sufficient

Answer (C)
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Re: A hot dog vendor who sells only hot dogs and soft drinks charges $3 [#permalink] New post  07 Jul 2015, 05:11
Bunuel wrote:
A hot dog vendor who sells only hot dogs and soft drinks charges $3 for a hot dog. If the vendor collected $1,000 in total revenue last month, how much does he charge for a soft drink?

(1) The vendor sold twice as many hot dogs as soft drinks last month.
(2) The revenue from hot dog sales last month was 3/4 of the total monthly revenue.


Kudos for a correct solution.


Let n be the numbe rof hot dogs sold last month. Let m and p be the number and price of soft drink respectively last month.

Thus, per the question 3n+mp =1000 and p=?

1. Per statement 1, n=2m.

This reduces the above equation to:

1000 = m(6+p) this is still 1 equation with 2 variables. Thus not sufficient.

2. 3n= 0.75*1000 , this gives the value of n=250

Still the above equation 3n+mp=1000, has 2 variables remaining (m,p) but only 1 equation. Thus not sufficient.

Combining 1 and 2,

n=250, n=2m >> m=125

Substituting these values in the main equation, 3n+mp=1000, we get p=2$. Hence C is the correct answer.
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Re: A hot dog vendor who sells only hot dogs and soft drinks charges $3 [#permalink] New post  07 Jul 2015, 07:46
Bunuel wrote:
A hot dog vendor who sells only hot dogs and soft drinks charges $3 for a hot dog. If the vendor collected $1,000 in total revenue last month, how much does he charge for a soft drink?

(1) The vendor sold twice as many hot dogs as soft drinks last month.
(2) The revenue from hot dog sales last month was 3/4 of the total monthly revenue.


Kudos for a correct solution.


Let numbers of Hot Dogs be x and numbers of soft drinks be y while the price of a soft drink shall be S.

Statement 1:
3x+ys = 1000
Insufficient. 3 unknown, 1 equation. We do not know how many hot dogs, therefore, we don't know how many soft drinks have been sold.

Statement 2:
3x=3/4*1000
x=250

Gives us the number for hot dogs. Alone insufficient.

Together we have:

250 hot dogs for $3. According to statement 1; No of Soft drinks = 250/2 = 125
Together we can evaluate the price of a soft drink.

Hence Answer Choice C
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Re: A hot dog vendor who sells only hot dogs and soft drinks charges $3 [#permalink] New post  07 Jul 2015, 08:34
Bunuel wrote:
A hot dog vendor who sells only hot dogs and soft drinks charges $3 for a hot dog. If the vendor collected $1,000 in total revenue last month, how much does he charge for a soft drink?

(1) The vendor sold twice as many hot dogs as soft drinks last month.
(2) The revenue from hot dog sales last month was 3/4 of the total monthly revenue.


Kudos for a correct solution.


Let
H = Number of Hot Dog Sold
S = Number of Soft Drink Sold and X = Price of Each Soft Drink

3H + SX = 1000 ---- Given

We need to find X

To find X, we need H and S.

Statement 1 :
H = 2S

Substituting in Given Equation we get
S(6+ X) = 1000

two variable One equation, hence unique value of X cannot be determined. --- Insufficient

Stattement 2 :
Revenue from Hot Dog = 3/4 * Total
3H = 3/4 * 1000
Hence H = 250

Clearly not sufficient as we dont know the value of S. --- Insufficient

Combining Statement 1 and 2
H = 2S
and H = 250 Hence S = 125

Since we know H and S (2 out of 3 unknown) we can find the value of X.

Hence Option C
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Re: A hot dog vendor who sells only hot dogs and soft drinks charges $3 [#permalink] New post  07 Jul 2015, 10:19
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Bunuel wrote:
A hot dog vendor who sells only hot dogs and soft drinks charges $3 for a hot dog. If the vendor collected $1,000 in total revenue last month, how much does he charge for a soft drink?

(1) The vendor sold twice as many hot dogs as soft drinks last month.
(2) The revenue from hot dog sales last month was 3/4 of the total monthly revenue.


Kudos for a correct solution.


Price of Hot dog (H) = $3
Total Revenue collected = $1,000

Question : Price of Soft Drink (S) = ?

Statement 1: The vendor sold twice as many hot dogs as soft drinks last month.
let, no. of hot dogs sold last month = 2x
i.e. no. of Soft Drinks sold last month = x
i.e. 2x*3 + x*S = 1000
Two variables and one Equation here with infinite many solutions so
NOT SUFFICIENT

Statement 2: The revenue from hot dog sales last month was 3/4 of the total monthly revenue.
Revenue from Hot Dogs = (3/4)*1000 = 750
i.e. Revenue from Soft Drinks = (1/4)*1000 = $250

Also, No. of Hot dogs sold = Revenue from Hot Dogs / Price per hot dog = 750/3 = 250
But no. of Soft Drinks sold is unknown to answer. So
NOT SUFFICIENT

Combining The two statements
No. of Hot Dogs sold / 2 = No. of Soft Drinks sold= 250/2 = 125 [From Statement 1]
Revenue from Soft Drinks = No. of Soft Drinks sold * Price per Soft Drink = 125*S = $250 [From Statement 2]
i.e. S = $2
SUFFICIENT

Answer: Option C
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Re: A hot dog vendor who sells only hot dogs and soft drinks charges $3 [#permalink] New post  15 Dec 2015, 19:41
this question was the last after a bunch of tricky 700 level questions, and I was very suspicious of selecting C, yet it is the correct answer:
we can rewrite the first statement as: (6+n)D=1000. since we have 2 variables, we can't solve it.
statement 2 says that 750$ was made from hot dog sales. which means that drinks were 250$.
1+2 -> we have 250 hot dogs, which means that 125 drinks were sold. we have 250$ revenue from 125 drinks. the answer is 2$ per drink. the answer is C.
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Re: A hot dog vendor who sells only hot dogs and soft drinks charges $3 [#permalink]
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