A lemonade stand sold only small and large cups of lemonade

This problem is very good example how easy and quick plug-in method might be.

Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;

Let the price of small cup be $6, then the price of larges cup would be 7/6*6=$7;

Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$7=$28;

Fraction of total revenue from large cups: 28/(36+28)=7/16.

Answer: A.
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......................... Small .................... Large ............ Total

Sale .................... \(\frac{3x}{5}\) ..................... \(\frac{2x}{5}\) ................. x (Assume)

Price ..................... a .......................... \(\frac{7a}{6}\)

Required Fraction\(= \frac{\frac{2x}{5} * \frac{7a}{6}}{\frac{3xa}{5} + \frac{14xa}{6}} = \frac{14xa}{30} * \frac{30}{32xa} = \frac{7}{16}\)

Let total no. of cups be x
Small cups ( \(\frac{3}{5} x\)) \(+\) Large Cups (\(\frac{2}{5} x\)) \(= x\)

Let the price of small cups be \(y\)
then price of large cups be \(\frac{7}{6} y\)

Therefore required fraction = (Price of large cups * no. of large cups) / (Price of large cups * no. of large cups + Price of small cups * no. of small cups)

= \(\frac{\frac{2}{5} x * y}{\frac{2}{5}x * \frac{7}{6}y + \frac{3}{5} x * y}\)


= \(\frac{\frac{7}{15} xy}{\frac{7}{15} xy + \frac{3}{5} xy}\)


= \(\frac{xy * \frac{7}{15} }{xy * \frac{7}{15} + \frac{9}{15}}\)


= \(\frac{7}{16}\)

therefore answer is A

We can let the total number of cups = n. Since 3/5 of the cups that were sold were small, (3/5)n = the number of small cups sold and (2/5)n = the number of large cups sold.

Also, if we let the price of each small cup = p, then the price for each large cup = (7/6)p.

The revenue from the sale of large cups is (7/6)p * (2/5)n = (7/15)np and the revenue from the sale of small cups is p * (3/5)n = (3/5)np. Therefore, the total revenue from the sale of all the cups is (7/15)np + (3/5)np = (7/15)np + (9/15)np = (16/15)np.

We can now determine what fraction of Tuesday's total revenue was from the sale of large cups.

[(7/15)np]/[(16/15)np] = (7/15)/(16/15) = 7/16

Alternate Solution:

Let’s denote the total number of cups sold by 5n in which n is an integer. Since 3/5 of the number of cups sold were small, the number of small cups that were sold is (5n)(3/5) = 3n. Similarly, since 1 - 3/5 = 2/5 of the number of cups sold were large, the number of large cups that were sold is (5n)(2/5) = 2n.

Also, let’s denote the price of each small cup as6p. Then, the price of a large cup was (6p)(7/6) = 7p.

Now, the revenue earned from small cups was (3n)(6p) = 18np and the revenue earned from large cups was (2n)(7p) = 14np. In total, a revenue of 18np + 14np = 32np was earned. The large cups constituted 14np/32np = 7/16 of this revenue.

Answer: A
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Hey
In the numerator I guess, the price of large cup should be 7/6y and not just y.
Please Check!
Regards

My solution:
3/5 are small, 2/5 large.

Revenue from small cups = 3/5 * 6/6 = 3/5 (It remains the same fraction because we multiply by 6/6=1)
Revenue from large cups = 2/5 * 7/6 = 7/15

Total revenue = 3/5 + 7/15 = 16/15

For solve this problem we need: Revenue from large cups / Total revenue.

So: 7/15/(16/15) = 7/15 * 15/16 = 7/16 --> Answer A

Bunuel

I understand that the Fraction we need is: (Large Cup Sale * Large Cup Price) / (Small Cup Sale * Small Cup Price) + (Large Cup Sale * Large Cup Price).
Now I don't understand, why the Large Cup term in the denominator is \(\frac{14xa}{6}\) and not \(\frac{7xa}{15}\) or \(\frac{14xa}{30}\).
Please help me out.

Lets take 5 as total cups, as question uses fractions 3/5

Large Cup = 2
Small cups = 3
Total 5

LC = 3 * 1 = 3
SC = 2 * 7/6 = 7/3

Total = 16/3

LC/Total = 7/3 divided by 16/3 = 7/16
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given
qty of large cups 2/5 & 3/5 of small
let total cups be 5 ; large ; 2 and small ; 3
cost of small cup ; 6 so large cup cost ; 7
revenue from large cup ; 7*2 ; 14 and small cup revenue ; 6*3 ; 18
total revenue ; 14+18 ; 32
fraction of Tuesday's total revenue was from the sale of large cups

14/32 ; 7/16
OPTION A

Unit for Large cup = L, Unit of small cup = S and T= L+S where T is the total cups sold
Price per unit large = l, price per unit small = s

Total revenue = R = lL+sS

Small cups(S) = 3/5T , Thus, Large cups(L) = 2/5T

l=7/6s (mentioned in question)

Question has asked what is the contribution of large cup in tuesday's revenue which means :

Revenue from sale of large cup / Total revenue is

Putting all values in the equation :

=Ll/(Ll+Ss)
=(2/5T*7/6s) / [(2/5T*7/6s) + (3/5T*s)]
=7/16

OA (A)

Bunuel i make this mistake " If the large cups were sold for 7/6 as much as the small cups" of interpreting this statement in quotes i.e. to add 7/6 x +x , whereas it is only 7/6x. Could you advise how do i rectify this problem, how will GMAT pose the statement for x+7/6x and only 7/6x.

Using a chart to arrange the information and plugging in values on your own can get the answer faster. See the solution below:

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