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GMAT Focus DS Percentage Question

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by bryan22583 » Tue Apr 16, 2013 12:07 pm
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 store's gross profit last May less than its gross profit last April?

1) The store's revenue last May was 2,400$ less than its revenue last April
2) The store's expenses last May were 4 percent less than its expenses last April

Answer: B

I understand that (1) is clearly insufficient, but I'm hoping that an expert can show me a fast way to evaluate statement (2). Thanks in advance for any help!
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by srcc25anu » Tue Apr 16, 2013 2:17 pm
ST2 is sufficient by itself.

Gross Profit = revenue - Expense
May Revenue = 6% less than April Revenue. suppose April Rev = 100 and MAy Revenue = 94
May Expense = 4% less than April Expense. Suppose April EXPENSE = 50 And May expense = 48
GP (MAy) = 94 - 48 = 46
GP (April) = 100 - 50 = 50
GP (April) > GP (May)

alternate way to think: revenue declined by a greater % than costs hence GP should be lower.
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by GMATGuruNY » Wed Apr 17, 2013 3:21 am
bryan22583 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 store's gross profit last May less than its gross profit last April?

1) The store's revenue last May was 2,400$ less than its revenue last April
2) The store's expenses last May were 4 percent less than its expenses last April

Answer: B

Statement 1: The store's revenue last May was 2,400$ less than its revenue last April.
No information about the change in expenses from April to May.
INSUFFICIENT.

Statement 2: The store's expenses last May were 4 percent less than its expenses last April.
Let R = April's revenue and E = April's expenses.
According to the question stem, May's revenue was 6% less: .94R.
According to statement 2, May's expenses were 4% less: .96E.
Profit = revenue - expenses.
For April's profit to be LESS THAN OR EQUAL TO May's profit, the following would have to be true:
R - E ≤ .94R - .96E
.6R ≤ .4E
R ≤ (2/3)E.
Not possible: the question stem indicates that R>E.
Since it is not possible that April's profit was less than or equal to May's profit, April's profit must have been GREATER than May's profit.
SUFFICIENT.

The correct answer is B.
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