Warehouse W's revenue from the sale of sofas was what percen

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Warehouse W's revenue from the sale of sofas was what percent greater this year than it was last year?

1) Warehouse W sold 10% more sofas this year than it did last year
2) Warehouse W's selling price per sofa was $30 greater this year than it was last year

We need to find the percentage increase in the revenue of Warehouse X. This would normally be calculated as (X-Y)/X where would be the revenue this year and y would be the revenue last year.
Remember, Total revenue= Number of sofas sold * cost of sofas

Let us analyze the options now
1) This tells is about the percentage increase in sale of sofas. However, even though we know about the percentage increase in the number of sofas sold, we do not know anything about the selling price of these sofas in either years and hence, information is insufficient.

Statement 2) also gives us information about the difference in selling price per sofa in both years. However, we do not know the number of sofas sold. INSUFFICIENT.

Together,
we know that the price of the sofa increase by $30 this year. We also know something about the percentage increase in the number of sofas sold.
Let us consider the number of sofas sold to be x last year. The number of sofas sold this year would be 1.1x. Now, let us consider the price of sofa last year to be y. The current price of the sofa would be y+30.
Percentage change would involve two different variables as shown below

(1.1x(y+30)-xy)/xy
All terms might cancel out but we will be left with a 30/y and since, we do not know the value of these variable, it would not be possible to calculate the percentage change. INSUFFICIENT
Answer is E.
Method 2)

Another way to solve this problem is to imagine, the increase in price.
Statement 1) would turn out to be insufficient because of the reason statement above.
Statement 2) gives us the increase in the price of the sofa. However, the 30 increase might be a huge increase if the beginning price of the sofa was $40. However, if the beginning price of the sofa was $300, then the percentage change would be very small.

Together, by reasoning similar to 2), the percentage change in the revenue might be very big or very small depending on the last year price of sofas. Hence, INSUFFICIENT.

This question could have been solved if the statements had given us either percentages in both statements or exact values in both statements.

Hope this helps! Let me know if I can help you any further.

Another for E,

to answer the question we need to know either percent change in BOTH price and quantity (revenue=price x quantity) or exact values of prices and quantities.

im getting E. Here's what I did:

we are looking for (a-b)/b, where a is revenue this year and b is revenue from last year.

from stat 1, we only know the increase in sales volume, but nothing about the price. We need price for revenue calculation, and so this is insuff.

from stat 2, we know that new price=old price + 30, but nothing about how many were sold in each year. Insuff.

Together, we know that a=(x+30)(1.1m) where m=couches sold last year, x=price last year and b=(x)(m). We end up with:

(x+30)(1.1m)-(x)(m) / (x)(m) --> 0.1 + (33/x) .... we still have one variable left over, so we cant solve.

This can quickly be deduced to either C or E.

Now lets say S=# of sofas and P= price

So R should equal S(P)

For this year the equation R=1.10S(P+33)

From this we don't really get any info.

So I say E.

That is the OA, nice job.

Had we been provided with the % price increase rather than $ amount, would C be the answer or still E?

so if they provided a similar relation of cost as they did in statement 1 it would have been sufficient?

1) Warehouse W sold 10% more sofas this year than it did last year
2 ) The price this year is 30 percent higher than last year

Yes, in such a case the statements together would have been sufficient.
Let us try analyzing the situation you mentioned.

statement 1) is still insufficient since we do now know anything about the total revenue. Foe example, the change in selling price of the sofas could be 100% or even as small as 10%. Depending on the percentage increase in selling price, the percentage change in revenue would have to be calculated.
Statement 2) is still insufficient since all we know about is the percentage change in selling price. However, we still do not know much about the percentage increase in the number of sofas sold. For example, if the number of sofas sold increased by 80%, the percentage change would be very high. On the other hand, if it was as low as 10%, the percentage change could be lower.
However, note that we need to find a particular value of percentage change in the revenue. This percentage change cannot be found using either data alone.

Taking the statements together, we know the exact percentage change in the number of sofas(x and 1.1x) sold and the percentage increase in selling price(y and 1.3y). Hence, the percentage increase can be calculated and would be of the form
(1.1x*1.30y-xy)/xy
We can calculate a specific value for this and hence these statements are sufficient together.

Hope this helps! Let me know if I can help you any further.

Let the no of sofas sold last year be = N
Price during last year = P
Total Revenue (Last year) = NP

Statement 1
no of sofas sold (current year) = 1.1N
We don't know the price of sofa this year
Thus Insufficient

Statement 2
Price during current year = P + 30
We don't know the no of sofa's sold this year.
Thus Insufficient

Statement 1& 2
Total Revenue (Current year) = 1.1N(P+30)

Percent change = (1.1NP +33-NP)/NP
=(0.1NP + 33)/NP
Still we don't have the value of NP.
Thus Insufficient
Answer E

For this questions regarding percent change in revenue we always need the two ratios from price and quantity between both years, one and an absolute difference 30$ doesn't help. Keep this in mind and reduce your average time for this type of questions.

Cheers
J

1) and 2) alone are definitely insufficient

when we combine them: let the units sold last year be x, so this year 1.1x units must have been sold.
let the price per unit last year be y, so this years price would be (y+30)
=> last year's sale= xy.
this year's sale = 1.1xy + 33x
% change = (0.1y + 33)/y %
we don't have any info about y, hence insufficient.

so, E.
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Revenue = Sofas X Price

Revenue Change = [Revenue This Year / Revenue Last Year] - 1

For statement 1
R= Sofas Sold
P2 = Price Year 2
P1 = Price Year 1

For Statement 2
R2= Sofas Sold year 2
R1 Sofas Sold Year 1
P= Price

For Statement 3
R= Sofas Sold
P = Price

We can begin by defining some variables.

a = quantity of sofas sold last year

b = price per sofa sold last year

c = quantity of sofas sold this year

d = price per sofa sold this year

We need to determine what percentage greater this year’s sofa revenue was than last year’s. To determine the percentage increase, we can use the percent change formula. Recalling that revenue = price x quantity, we see that the revenue from sofas sold last year is ab and the revenue from sofas sold this year is cd.

percent change = (new – old)/old x 100

(cd – ab)/ab x 100 = ?

(cd/ab – 1) x 100 = ?

100cd/ab – 100 = ?

Statement One Alone:

Warehouse W sold 10 percent more sofas this year than it did last year.

Using the information in statement one, we can create the following equation:

c = 1.1a

Without knowing the values of b and d, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Warehouse W’s selling price per sofa was $30 greater this year than it was last year.

Using the information in statement two, we can create the following equation:

d = 30 + b

Without knowing the values of a and c, statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two together, we still do not have enough information to answer the question. Even if we substitute 1.1a for c and 30 + b for d in the expression 100cd/ab – 100, we are left with:

100(1.1a)(30 + b)/ab – 100

110a(30 + b)/ab – 100

110(30 + b)/b – 100

Since we don’t know the value of b, we can’t determine a unique value for the expression.

Answer: E
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This problem can be easily solved by plugging in values

Revenue(r) = number of sofas(n) * Price per Sofa(p)

St 1 : Not Sufficient as no information about Price per Sofa

St 2 : Not Sufficient as no information about Number of Sofas

St 1 and St 2 Combined :

Case 1 : n (last year) = 10 , n (this year) = 11 ( 10% increase)

p (last year) =10 , p (this year) = 40 ($30 increase)

r (last year) = 100 , r (this year = 440 Percentage increase = 340%

Case 2 : n (last year) = 10 , n (this year) = 11 ( 10% increase)

p (last year) = 20, p (this year) = 50 ($30 increase)

r (last year) = 200 , r (this year) = 550 Percentage increase = 175%

Since, We are getting two different values

Not Sufficient

Choice E

Question: By what percent is Revenue this year > Last year?

Statement 1: Warehouse W sold 10 percent more sofas this year than it did last year.

Prices are unknown hence

NOT SUFFICIENT

Statement 2: Warehouse W’s selling price per sofa was $30 greater this year than it was last year.

Number of sofas is unknown hence

NOT SUFFICIENT

Combining the statements

SInce count of sofas is unknown hence

NOT SUFFICIENT

Answer: Option E

Asked:L Warehouse W’s revenue from the sale of sofas was what percent greater this year than it was last year?

R = P * Q
dR/R = dP/P * Q + dQ/Q * P

(1) Warehouse W sold 10 percent more sofas this year than it did last year.
There is no information about change in price of sofas
NOT SUFFICIENT

(2) Warehouse W’s selling price per sofa was $30 greater this year than it was last year.
There is no information about volume of sofas sold
NOT SUFFICIENT

(1) + (2)
(1) Warehouse W sold 10 percent more sofas this year than it did last year.
(2) Warehouse W’s selling price per sofa was $30 greater this year than it was last year.
dQ/Q = 10%
No information is provided for percentage change in prices of sofas
NOT SUFFICIENT

IMO E

The question is, can I tell by (i) what percent of revenue grew on sofas. It says its a 10% increase on sale, and does not say that SP increased. Why cant we assume it did not as its not mentioned?

When solving DS questions one of the most important things is that you should never assume any extra information that is not given in the question.
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Warehouse W's revenue from the sale of sofas was what percent greater this year than it was last year?

Warehouse W's revenue last year = No of sofas sold last year* Selling price of each sofa last year
Warehouse W's revenue this year = No of sofas sold this year* Selling price of each sofa this year

In order to compare both revenues , we need to know about no of sofas sold this year and last year as well as Selling price of each sofa this year and last year.

(1) Warehouse W sold 10% more sofas this year than it did last year
Statement 1 will give you comparison of no of sofas sold this year w.r.t last year but it doesn't give any info about the selling price of the sofa this year and the last year. Hence its insufficient.

(2) Warehouse W's selling price per sofa was $30 greater this year than it was last year
Statement 2 doesn't give any idea about the no of sofas sold. Hence,it's insufficient.

Combining both statements,
Let's say that the no of sofas sold last year = X
Selling price of each sofa last year = Y
Revenue from last year = X*Y
no of sofas sold this year = X + 10% of X= 1.1 X
Selling price of each sofa last year = Y + 30
Revenue from this year = 1.1X*(Y+30)
% increase in revenue =( (1.1X*(Y+30) - X*Y)/X*Y )* 100 = (.1 X*Y + 33*X)/X*Y * 100
We cannot find the % increase in the revenue as we don't know the value of Y.
So even though if you combine the statements, it's insufficient.

Option E is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME
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