M31-08

Question

A baker charges  x  dollars for a birthday cake. Next week, she plans to earn 320 dollars by selling cakes. If she were to reduce the price of the cake by 20 percent, she would need to sell two more cakes to generate the same revenue. How many cakes does she plan to sell next week?

A. 2
B. 4
C. 6
D. 8
E. 10

Bunuel · Accepted Answer

Official Solution:

A baker charges  x  dollars for a birthday cake. Next week, she plans to earn 320 dollars by selling cakes. If she were to reduce the price of the cake by 20 percent, she would need to sell two more cakes to generate the same revenue. How many cakes does she plan to sell next week?

A. 2
B. 4
C. 6
D. 8
E. 10

Reducing the price by 20% is equivalent to multiplying the price by  \frac{8}{10} . In this scenario, to achieve the same revenue, the baker must sell  \frac{10}{8}  times as many cakes. Essentially, we are told that  (	ext{number of cakes}) * \frac{10}{8} = (	ext{number of cakes}) + 2 , which implies that the number of cakes is 8.
 
Another way to look at this is by noting that when the price is reduced by 20%, it becomes 4/5th of the original price. To earn the same revenue, she must increase the quantity sold by 25% (the revenue must increase by 5/4 times to compensate for the reduction in price to 4/5th). From the question, we know that 25% of the original quantity equals 2. Thus, the total original quantity is 2 * 4 = 8.

Answer: D

ranaazad · Answer

Revenue = Price per cake * Number of cakes
Let T be the number of cakes being sold

So, x * T = .8x * (T+2)
=> T = 8

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Aryan19852 · Answer

price= 320/x 
new price= 320/0.80x equivalent to 400/x now difference is 80 and 2 additional cakes would cover it so price which is x would be 40 dollars now 320/40 gives us 8 cakes I hope this method is valid

SKDEV · Answer

Bunuel ,
This is confusing, I marked 10 (8+2) as I thought she implemented the plan of increasing cake by 2 next week

Bunuel · Answer

The key point is that the requirement to sell 2 more cakes if the price is reduced is a condition, not her actual plan. The baker's plan is to sell enough cakes at the current price to make $320. The additional 2 cakes come into play only under the hypothetical condition of a price reduction.

AryakiSekera · Answer

I don’t quite agree with the solution. the questions seems purposefully misleading. the last part does not specify clearly whether its referring to the first part or the second part of the question.

Bunuel · Answer

The baker’s plan is to make $320 at the current price, that’s the actual scenario. The mention of 2 extra cakes is a hypothetical used to set up the equation. The final question refers to the actual plan, not the hypothetical one. By the way, this has already been explained here: https://gmatclub.com/forum/m31-199466.html#p3437238

DeekshithaA · Answer

I like the solution - it’s helpful. wow, this is a really good question, would like to practise more such questions so that I learn to read mindfully.

Next week, she plans to earn 320 dollars by selling cakes - IF SHE WERE TO reduce the price of the cake by 20 percent - SHE WOULD NEED to sell two more cakes to generate the same revenue. How many cakes does she PLAN to sell next week?... HOLD ON TO HER PLAN. the rest is a hypothetical situation that is the supporting premise to get the answer.

ankitksingh · Answer

I like the solution - it’s helpful.

recusandaesaepe · Answer

I don’t quite agree with the solution. if number of cakes sold in a week = n
and cost of a given cake = c
Given: week 1 => 320=n*c
 week 2 => 320=(n+2)*.8C
Therefore: nc = (n+2)*.8C
 nc = .8nc + 1.6c
 .2nc = 1.6c
 .2n=1.6
 n=8

you then have to add 8+2 because the question asks for "how many cakes next week" being the week that she sold more cakes at a reduced cost.

Moreover this supports the 20% price reduction because assuming n=8, then c=40 in week 1 and 32 in week 2 and 32 is 20% less than 40

Bunuel · Answer

The question asks how many cakes she plans to sell next week under the original plan. The reduced-price case is only a  hypothetical condition  used to relate the quantities. So n is the planned number for next week, and n + 2 is the number she would need to sell if she reduced the price. Therefore the answer is 8, not 10.

By the way, this has already been explained twice above.

SS990 · Answer

Price per cake = 320/n
Price after reduction by 20% = 0.8 * 320/n=256/n
To maintain the same revenue, they have to maintain same cost per cake selling 2 more cakes = 320/(n+2)
so (256/n) = (320/n+2)
 Solving for this, we get n=8 (Option D)

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