Data Sufficiency

Hello all,

During a 1 day sale, a store sold each sweater of a certain type for $30 more than the store's cost to purchase each sweater. How many of these sweaters were sold during the sale?

1) During the sale, the total revenue from the sale of these sweaters was $270.
2) During the sale, the store sold each of these sweaters at a price that was 50 percent greater than the store's price to purchase them.

Why isn't the answer A?

From Question stem:
Selling Price (SP) = Cost Price + 30

From 1: -
Let x = # of sweaters sold
Revenue = SP(x) - CP(x)

270 = SP(x) - CP(x)
270 = (CP + 30)(x) - CP(x)
270 = CPx + 30x - CPx
270 = 30x
x = 9

9 Sweaters were sold. SUFF

From 2: -
SP = 1.5CP
CP + 30 = 1.5CP
CP = $60

We know the cost of each sweater and hence the selling price but that doesn't tell us the quantity sold!

Why isn't the answer A?

Statement (1) only tells us that the total revenue is $270.

Here are some scenarios consistent with the intro and statement (1):

- the store sold 1 sweater that it purchased for $240 and sold for $270.
- the store sold 2 sweaters that it purchased for $105 each and sold for $135 each.
- the store sold 3 sweaters that it purchased for $60 each and sold for $90 each.

As soon as there's more than 1 possible answer (i.e. we didn't need the 3rd example to move on with our lives), we know that statement (1) is insufficient.

Statement (2) tells us that the sale price of each sweater is 1.5 times the cost. Since we know that SP - cost = 30, that's enough information to calculate the sale price (2 equations, 2 unknowns). However, since we don't know how much money they either spent or brought in from sales, we can't calculate the # of sweaters.

If we combine the statements, we know from (1) that SP * # of sweaters = 270 and we know from (2) what the SP is. Therefore, combining the statements will give us enough information to calculate the # of sweaters sold.

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FYI - your error was in your original equation. SP(x) - C(x) doesn't equal total revenue, it equals total profit. Total revenue is simply SP(x).

Revenue = SP * quantity. You are computing it incorrectly.