During a one day sale, a store sold each sweater of a certain type for

During a one 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 thses 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% greater than the store's cost to purchase each sweater.

Given: \(p=c+30\)

(1) Revenue = price * # of sweaters sold --> \(270=p*n=(c+30)n\). Not sufficient to determine \(n\).

(2) \(p=1.5c=c+30\) --> \(c=60\). Not sufficient.

(1)+(2) \(c=60\) and \(270=(c+30)n=90n\) --> \(n=3\). Sufficient.

Answer: C.
_________________

S = selling price
C = cost price
\Question tells us S= C+30

st 1 = Selling price * no of sweaters = 270.............. insufficient
st 2 = S = 1.5C
using information from question
1.5 C = C+30
0.5C = 30
C = 60
S =90
but no clue on revenue or number of sweaters sold. ............. insufficient

together 90* no of sweaters = 270
no of sweater = 3
sufficient

hence C

(C)

Sale price = $30 + Cost price, or
S = $30 + C

1) Insufficient. Each sweater could have been sold for 60 or 230.
If n sweaters were sold, we have n*S = 270

2) Insufficient. 50% greater = $30, hence
or S = 1.5*C
Plugging this in the first equation, we get S = 90, C = 60. But we still don't have n.

Combining (1) & (2): n*90 = 270
or n = 3
_________________

1: revenue = profits - cost. 270$=(x+30)z z is the number of sweaters.

we have two unknowns and only 1 equation insuff.

2: x= cost. x+30=1.5x --> x=60 Thus total price is 90$. Insuff though b/c we dont know the revenue.

Together: 90z=270 --> z=3

C

Given: S = C + 30 [S = Sales, c = cost]

(1) NS=270 [N = number of sales]
So, (c + 30) x N = 270, N is unknown, Insufficient.

(2) c+30 = 150%c, C can be calculated from the equation, but we need N=? Insufficient.
C= 60
Considering C
(60+30) x N = 270
N = 3
_________________

Could you please explain :
Revenue = price * # of sweaters sold --> . Not sufficient to determine .

here We can consider Revenue is selling price - cost price , Can we ?

The total revenue from the sale is (price per unit) * (# of units sold).

(Selling price per unit) - (Cost price per unit) = (Gross profit from one unit).
_________________

Dear Bunuel,I follow the below way to answer the above question and I do not know what is the wrong in my way?

we have that (Selling price per unit) - (Cost price per unit) = (Gross profit from one unit)= 30

270= (Selling price per unit - Cost price per unit)*# of sweaters sold

270= 30*# of sweaters sold

So # of sweaters sold = 270/30

Hi 23a2012,

In your calculation, you're using the PROFIT to determine the number of sweaters sold, but the $270 mentioned in Fact 1 is based on the REVENUE.

The equation is supposed to be:

$270 = (Sale price per sweater)(number of sweaters).

GMAT assassins aren't born, they're made,
Rich

I feel confused,

For each sweater, the store can earn $30, so if we can get the revenue is $270, why we cannot say that they sold out 9 sweaters?

Hi haodong,

You're confusing REVENUE with PROFIT.

The prompt tells us that the PROFIT per sweater sold is $30. The information in Fact 1 tells us that the REVENUE generated was $270.

IF....
each sweater sold for $90, then $270/$90 = 3 sweaters were sold (and the profit was 3($30) = $90)
each sweater sold for $45, then $270/$45 = 6 sweaters were sold (and the profit was 6($30) = $180)

GMAT assassins aren't born, they're made,
Rich

Bunuel chetan2u VeritasKarishma

Isnt it true if the price is more than $30, there can only be one price for the sweater i.e. 90 given the number of sweaters sold have to be an integer. Unless he sells one sweater for $270 but the question states how many sweaters?

Hi gmatapprentice,

To answer your immediate question: YES - the number of sweaters MUST be an integer (for example, you can't buy "1/7 of a sweater" in these types of questions).

In my post (directly above yours), I included 2 different examples in which the selling price of a sweater was MORE than $30. There's actually another option though:

IF... each sweater sold for $135, then $270/$135 = 2 sweaters were sold (and the profit was 2($30) = $60)

GMAT assassins aren't born, they're made,
Rich

Missed your post somehow EMPOWERgmatRichC - thanks for the clarification all clear.

let purchase price = p
sale price = p + 30

How many of these sweaters were sold during the sale?

(1) Total revenue = $270

We don't know the purchase price. If the purchase price was $240, then only one sweater was sold. INSUFFICIENT.

(2) p + 30 = 1.5p
30 = 0.5p
60 = p
We know the purchase price is $60, from which we can conclude the sale price is $90. However, we don't know the total revenue. INSUFFICIENT.

(1&2) total revenue = $270; sale price = $90

We can conclude 3 sweaters were sold. SUFFICIENT.

Answer is C.
_________________

During a one 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?

Let SP be selling price of the sweater and Cp be the cost price of the sweater.
Its given that Sp = Cp + 30 and we are asked to find the no of sweaters sold ( Let it be N )

(1) During the sale, the total revenue from the sale of these sweaters was $270.
Revenue = N * SP = 270

Statement 1 is insufficient as we cant find the value of N

(2) During the sale, the store sold each of these sweaters at a price that was 50% greater than the store's cost to purchase each sweater.
Sp = Cp + 50 % of Cp

Its given in the question that SP is 30 $ more the Cp.
So we can say that 50 % of Cp = 30
Cp =60$
Sp = 60 + 30 = 90 $
Even though we got the value of Sp but still we cant find the value of N.
Hence statement 2 is insufficient

By combining statement 1 and 2, we will be able to find the value of N
N * Sp = 270 and Sp = 90

Option C is the answer

Thanks,
Clifin J Francis
GMAT SME

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________