A baker charges x dollars for a birthday cake. Next week, she intends

Assume number of cake sale = n, Price/cake = x

x*n=320;
Reduced cake price= 0.8 *x, then number will increase by two so (n+2) => (n+2)*0.8x=320

Equating above both equation, x*n=(n+2)*0.8x ; solving this equation we get n=8

Hence answer is D

Thanks,

Let number of cake be n and cost of a cake be x

hence, nx=320.......(1)
Now, (n+2)*0.8x=320
thus, x=40
n=8
(D)

Hi All,

Many Test Takers would take an Algebraic approach with this question (which is fine). Sine the answers are NUMBERS, and we're asked for the number of cakes the baker intends to sell, we can TEST THE ANSWERS.

We're told that by selling cakes at X dollars/cake, a baker will make $320.
Reducing the price by 20% and selling 2 MORE cakes will also make her $320.

We're asked for the original number of cakes that the baker intends to sell.

$320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....

Let's TEST ANSWER D: 8 cakes

IF....
Original cakes = 8
8(X) = $320, so X = $40/cake
20% off = $8 off = 40-8 = $32/cake
+2 more cakes = 8+2 = 10 cakes
10(32) = $320

This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

The answer is D
let n=the number of birthday cake
so the number of cake will be sell next week=n+2
x*n=320
80%x*(n+2)=320
4/5x(n+2)=n*x
4/5(n+2)=n
4/5n+8/5=n
8/5=n-4/5n
8/5=n/5
5n=40
n=8

Ans: D

Solution: Equation based question : if price is reduced by 20% then selling price= 256
now she has to sell two more = n+2
now
256*(n+2)=360*n
n=8

Let No of cakes = C
Price of a cake = X

So C*X=320 --------- (1)

If price of a cake is decreased by 20 %, New price will be 0.80 of X

So 0.80 X ( C+2 ) = 320 ------------ (2)

Solving (1) and (2) we get

X= 40 and C = 8.

Hence (D. 8) is the correct answer

I think the question is asking us to find out N+2 as we need to find out the number of cakes she needs to sell next week .... Thus it must be 8+2 = 10

Hence Answer should be E

THIS QUESTION CAN BE SOLVED WITHOUT USING 320$ OR x $--- Data Sufficiency point of view

Price is reduced by 20% and therefore, to earn the same revenue she must increase the quantity sold by 25%. Thus, from the question, 25% of original quantity = 2. Thus total original quantity = 2*4 = 8 Option D

Alternatively: revenue = price * quantity. Let price = quantity = 10
Thus, revenue = 100
New price = 8 and let new quantity be q
Since revenue is constant, we have 100= 8* q
Thus q = 12.5
Change in quantity = 12.5 - 10 = 2.5
Now when change in quantity is 2.5, original quantity is 10
Thus when change is quantity is 2 (as per the question), required original quantity = (10/2.5)*2 = 8 Option D

KUDOS PLEASE!!

We can create the equations in which c = number of cakes she intends to sell next week:

xc = 320

x = 320/c

and

(0.8x)(c + 2) = 320

0.8xc + 1.6x = 320

Substituting we have:

0.8(320) + 1.6(320/c) = 320

256 + 512/c = 320

512/c = 64

512 = 64c

c =512/64 = 8

Answer: D

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.