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Math Expert V
Joined: 02 Sep 2009
Posts: 59722
Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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1 00:00

Difficulty:   55% (hard)

Question Stats: 69% (02:13) correct 31% (02:38) wrong based on 118 sessions

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Java House charges $3.25 for a cup of coffee that costs a total of$2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs$2.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

A. 7,858
B. 8,301
C. 14,667
D. 63,840
E. 146,667

Kudos for a correct solution.

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Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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2
Bunuel wrote:
Java House charges $3.25 for a cup of coffee that costs a total of$2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs$2.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

A. 7,858
B. 8,301
C. 14,667
D. 63,840
E. 146,667

Kudos for a correct solution.

Java: Profit/Cup = 3.25-2.85 = 0.4
: No of Cups = 55,000
: Gross Profit = 55,000*0.4 = 22,000

Joe: Profit/Cup = 0.15
: Gross Profit = 22,000
: No of Cups = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)

A Short Cut: Just based on profit per cup of java v/s that of joe, we know that total number of cups for joe has to much greater than that of java to make same amount of profit. Easily eliminates A,B,C. Now D is still too small because profit/cup for joe is less than half of that of java so by that rationale no. of cups for joe should be more than double for that of java... only logical answer seems to be E.
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Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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1
Gross Profit made by Java House = ( 3.25 - 2.85 ) * 55000

Gross Profit made by Cup O joe house = (2.80 - 2.65 ) * X , where X is the number of cups Cup O joe needs to sell .

In order for Cup O Joe of break even with Java House equate the two equations

( 3.25 - 2.85 ) * 55000 = (2.80 - 2.65 ) * X

X = (0.4 * 55000 ) / 0.15
= 146,666.4 .

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Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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Profit earned by Java $$= (3.25 - 2.85) * 55000 = 55000 * \frac{40}{100} = 22000$$

Sale required to earn this much profit $$= \frac{22000}{2.80-2.65} = \frac{22000}{0.15} = 22 * \frac{10^5}{15} = 1.4xxxx * 10^5 = 14x,xxx$$

Answer has to be 6 digits, starting from 14

Only option E qualifies
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GMAT 1: 700 Q44 V41 Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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1
JH profit = .40 per cup
COJ profit = .15 per cup
Since JH makes nearly 3x more per cup, COJ must sell nearly 3x as many cups to make the same amount.
55,000 * 2 2/3 = 146,667
E
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Posts: 9876
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Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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1
devilbart wrote:
Bunuel wrote:
Java House charges $3.25 for a cup of coffee that costs a total of$2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs$2.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

A. 7,858
B. 8,301
C. 14,667
D. 63,840
E. 146,667

Kudos for a correct solution.

Java: Profit/Cup = 3.25-2.85 = 0.4
: No of Cups = 55,000
: Gross Profit = 55,000*0.4 = 22,000

Joe: Profit/Cup = 0.15
: Gross Profit = 22,000
: No of Cups = 22,000/0.15 = 220,000/1.5 (only closes is 146,667)

A Short Cut: Just based on profit per cup of java v/s that of joe, we know that total number of cups for joe has to much greater than that of java to make same amount of profit. Easily eliminates A,B,C. Now D is still too small because profit/cup for joe is less than half of that of java so by that rationale no. of cups for joe should be more than double for that of java... only logical answer seems to be E.

You can reduce the calculations significantly by leaving the large numbers for the end.

Java's profit per cup is 0.4 and Joe's profit per cup is 0.15. So for every cup that Java sells, Joe must sell .4/.15 = 8/3 cups to get the same profit.
So if Java sells 55,000 cups, to get the same profit, Joe must sell
55000*8/3 which is certainly more than twice of 55,000 so only option (E) is possible.
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Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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Indeed. I only used the shortcut i mentioned but then did the full calculation to "Explain" the answer.
Math Expert V
Joined: 02 Sep 2009
Posts: 59722
Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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Bunuel wrote:
Java House charges $3.25 for a cup of coffee that costs a total of$2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs$2.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

A. 7,858
B. 8,301
C. 14,667
D. 63,840
E. 146,667

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Explanation: From the given information, we know that Java House earns $0.40 profit per cup of coffee, and sells 55,000 cups. We also know that Cup 'O' Joe earns$0.15 profit per cup, and we're asked for the number of cups that it must sell for its profits to equal those of Java House. Accordingly, Java House's profits ($0.40 * 55,000) must equal Cup 'O' Joe's ($0.15 * x cups). Performing the calculations to solve for x, we find that $22,000 =$0.15x, and that x must equal 146,667. As a result, the correct answer is E.
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Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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Bunuel wrote:
Java House charges $3.25 for a cup of coffee that costs a total of$2.85 to make. Cup'O'Joe charges $2.80 for a cup that costs$2.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does?

A. 7,858
B. 8,301
C. 14,667
D. 63,840
E. 146,667

Kudos for a correct solution.

oh damn..I spent an extra time to figure out that I don't need to check "HOW MANY MORE THAN JH, COJ needs to sell.." thus, I was looking for some number ~90k, but then realized how stupid I am...
ok...
3.25$charges, 2.85$ costs, profit margin - 0.4$COJ - 2.80$ charges, costs 2.65$. profit margin-0.15$

now, JH sells 55k -> gross profit will be 55k*0.4$or 22k$.
now, COJ needs to sell 22k/0.15$or 146,666.666... so smth around 146,667 cups. E Target Test Prep Representative V Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8692 Location: United States (CA) Re: Java House charges$3.25 for a cup of coffee that costs a total of $2. [#permalink] ### Show Tags Bunuel wrote: Java House charges$3.25 for a cup of coffee that costs a total of $2.85 to make. Cup'O'Joe charges$2.80 for a cup that costs $2.65 to make. If Java House sells 55,000 cups of coffee, how many must Cup'O'Joe sell to make at least as much in total gross profit as its competitor does? A. 7,858 B. 8,301 C. 14,667 D. 63,840 E. 146,667 The profit per cup for Java House is 3.25 - 2.85 =$0.40.

So they make a total of 55,000 x 0.4 = $22,000 gross profit. The profit per cup for Cup’O’Joe is 2.80 - 2.65 =$0.15.

So they must sell a total of 22,000/0.15 = 146,667 cups of coffee.

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Re: Java House charges $3.25 for a cup of coffee that costs a total of$2.  [#permalink]

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