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by parulmahajan89 » Thu Nov 14, 2013 5:54 pm
During a one day sale,a store sold each sweater of a certain type for $30 more than store's cost of purchasing these sweaters. How many of these sweaters were sold during the sale.

1.During the sale,the total revenue of sale was $270
2.During the sale,the store sold each of these sweaters at a price that was 50 percent greater than store's cost to purchase each sweater
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by Uva@90 » Thu Nov 14, 2013 8:15 pm
parulmahajan89 wrote:During a one day sale,a store sold each sweater of a certain type for $30 more than store's cost of purchasing these sweaters. How many of these sweaters were sold during the sale.

1.During the sale,the total revenue of sale was $270
2.During the sale,the store sold each of these sweaters at a price that was 50 percent greater than store's cost to purchase each sweater
Hi Parulmahajan89,
Let X be the cost for which Store has Purchased.
and N be the number of Sweaters sold.

Given: Store sold sweater for X+30 $

To Find: N

Statement1: During the sale,the total revenue of sale was $270
So, 270 = (X+30)*N
Two variable and one equation insufficient.

Statement 2: During the sale,the store sold each of these sweaters at a price that was 50 percent greater than store's cost to purchase each sweater

1.5X =X+30
So X = 60
we don't know N
so Insufficient.

1+2
from 1 we know 270 = (X+30)*N
and from 2 we know X = 60
so we can solve for N
Hence sufficient.

Aside: 270 = (60+30)*N ==> N= 3
So shop sold 3 Sweaters.

Hope it helps you.

Regards,
Uva.
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by [email protected] » Thu Nov 14, 2013 11:49 pm
Hi parulmahajan89,

Uva@90 has provided a solid "math" explanation to this DS question. Here's how you can TEST Values to get the same result:

We're told that the "sell price" for a sweater was $30 MORE than the purchase price. We're asked HOW MANY sweaters were sold.

Fact 1: Total revenue from the sweaters was $270.

This tells us that the "sell price" was some FACTOR of 270 (and is at least $30).

So, the "sell price" could have been:
$90, in which case we sold 3 sweaters.
$45, in which case we sold 6 sweaters.
There are other possibilities, but we don't need to think about them right now.
Fact 1 is INSUFFICIENT

Fact 2: the "sell price" was 50% greater than the purchase price.

Combined with the information from the prompt (the "sell price" was $30 more than the purchase price)

Here, the "sell price" was:
S = 1.5P
S = P + 30
This is a "system" of equations (2 variables, 2 unique equations....I can solve it)
Sell Price = 90, Purchase Price = 60

However, we do NOT know how many sweaters were sold.
Fact 2 is INSUFFICIENT

Combined, we know that the revenue was $270 and the Sell Price was $90, so we know that 3 sweaters were sold.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich[/spoiler]
Last edited by [email protected] on Fri Nov 15, 2013 1:44 pm, edited 1 time in total.
Contact Rich at [email protected]
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by Uva@90 » Fri Nov 15, 2013 3:23 am
[email protected] wrote:Hi parulmahajan89,

Uva@90 has provided a solid "math" explanation to this DS question. Here's how you can TEST Values to get the same result:

We're told that the "sell price" for a sweater was $30 MORE than the purchase price. We're asked HOW MANY sweaters were sold.

Fact 1: Total revenue from the sweaters was $270.

This tells us that the "sell price" was some FACTOR of 270 (and is at least $30).

So, the "sell price" could have been:
$90, in which case we sold 3 sweaters.
$45, in which case we sold 6 sweaters.
There are other possibilities, but we don't need to think about them right now.
Fact 1 is INSUFFICIENT

Fact 2: the "sell price" was 50% greater than the purchase price.

Combined with the information from the prompt (the "sell price" was $30 more than the purchase price)

Here, the "sell price" was:
S = 1.5P
S = P + 30
This is a "system" of equations (2 variables, 2 unique equations....I can solve it)
Sell Price = 90, Purchase Price = 60

Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich[/spoiler]
Rich,
We are asked to find the Number of Sweater not Purchase Price or Selling Price.

Hence Statement 2 is Insufficient.

Combining 1 and 2 is sufficient to find

Hence, Answer is C

Regards,
Uva.
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by [email protected] » Fri Nov 15, 2013 1:42 pm
Hi Uva@90,

You're absolutely correct; I jumbled my information and lost sight of the question. I've gone back and updated my explanation.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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