Data Sufficiency

richachampion wrote:A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the stores gross profit last May less than its gross profit last April?

(1) The stores revenue last May was $2,400 less than its revenue last April.
(2) The stores expenses last May were 4 percent less than its expenses last April.

It is clear that statement 1 alone cannot help since the information about the expenses is not given.

S2: Say Revenue in Apr = 100, thus Revenue in May = 100-6 =94.

Again, say Expenses in Apr = x (given that x < 100), thus Expenses in May = x - 4% of x = 0.96x.

=> Profit in Apr = 100 - x and profit in May = 94 - 0.96x

We have to see whether 94 - 0.96x < 100 - x

=> 0.04x < 6

=> x < 6/0.04 => x < 150

x < 150 implies that if expenses in April in less than 150, the condition holds. We already know that x < 100, thus it is true.

Hope this helps!

-Jay

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richachampion wrote:A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the stores gross profit last May less than its gross profit last April?

(1) The stores revenue last May was $2,400 less than its revenue last April.
(2) The stores expenses last May were 4 percent less than its expenses last April.

We can start by using the following variables:

a = revenue last April

b = expenses last April

c = revenue last May

d = expenses last May

We are given that a clothing store's revenue last May was 6 percent less than its revenue last April. Thus,

c = 0.94a

We are also given that the store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Thus:

c > d and a > b

We need to determine whether a - b > c - d, or

Is a - b > 0.94a - d ?

Is 0.06a > b - d ?

Statement One Alone:

The store's revenue last May was $2,400 less than its revenue last April.

We can create the following equation:

c = a - 2,400

Since c = 0.94a, we can substitute 0.94a for c in the above equation and we have:

0.94a = a - 2,400

2,400 = 0.06a

a = 40,000 and c = 37,600

However, we still cannot determine whether 0.06a > b - d. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The store's expenses last May were 4 percent less than its expenses last April.

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

d = 0.96b

We can substitute 0.96b for d in the inequality question and we have:

Is 0.06a >b - 0.96b ?

Is 0.06a > 0.04b

Is 6a > 4b ?

Since we are given that a IS GREATER THAN b, then 6a MUST BE GREATER THAN 4b. Statement two alone is sufficient to answer the question.

Answer: B