Warehouse W's revenue (GMAT PREP 1)

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 am; Thanked: 48 times; Followed by:16 members

Warehouse W's revenue (GMAT PREP 1)

by alex.gellatly » Fri Aug 03, 2012 11:00 pm

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 percent more sofas this year than it did last year.
2. Warehouse W's selling price per sofa was $30 greater this year that it was last year.

I was starting to run low on time here. Is there a strategy to know which info one must have to solve percentage change DS question?

Thanks

A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231

Quote

Source: Beat The GMAT — Data Sufficiency | Fri Aug 03, 2012 11:00 pm

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pm; Thanked: 339 times; Followed by:49 members; GMAT Score:770

by eagleeye » Sat Aug 04, 2012 8:08 am

alex.gellatly wrote: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 percent more sofas this year than it did last year.
2. Warehouse W's selling price per sofa was $30 greater this year that it was last year.

I was starting to run low on time here. Is there a strategy to know which info one must have to solve percentage change DS question?

Thanks

I typically consider them on a case by case basis. But here, to find the percentage change, we need either:

1. The original and final revenues, OR
2. The %age change in prices per sofa and %change in number of sofas sold.

We should be able to reason this one out.

Here:
1. Warehouse W sold 10 percent more sofas this year than it did last year.
This is insufficient because we don't know how much more the sofas sold for this year.

2. Warehouse W's selling price per sofa was $30 greater this year that it was last year.
This is insufficient because we don't know how many sofas sold this year.

After quickly eliminating the two, we consider them together.

The first one gives us that we sold 10% more sofas.
Let's say we sold 10 sofas last year. so this year we sold 11.
Also price last year was 30$ less. Now, if we sold the sofas for a million dollars each last year, we are not going to have such a big percentage change in revenue.

However, if we gave away the sofas for free last year, the percentage increase is infinite.
Clearly both statements together are insufficient.

E is correct.

(Now if statement 2 said 30% higher price instead of 30$ per sofa, the answer would be C because we would have the percentage change in both parts of the revenue).

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Mon Dec 18, 2017 9:31 am

eagleeye wrote:
alex.gellatly wrote: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 percent more sofas this year than it did last year.
2. Warehouse W's selling price per sofa was $30 greater this year that it was last year.
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