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# To raise funds, a racing team sold T-shirts imprinted with

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Senior Manager
Joined: 10 Apr 2012
Posts: 278
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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30 Oct 2013, 09:49
4
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:39) correct 33% (01:25) wrong based on 306 sessions

To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of $100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x? 1. The team purchased 200 T-shirts, sold each T-shirt for$12, and made a $900 profit. 2. In addition to the$100 setup fee, the team paid $7 for each T-shirt. [Reveal] Spoiler: OA Last edited by guerrero25 on 30 Oct 2013, 16:01, edited 1 time in total. Magoosh GMAT Instructor Joined: 28 Dec 2011 Posts: 4677 Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink] ### Show Tags 30 Oct 2013, 10:43 5 This post received KUDOS Expert's post 1 This post was BOOKMARKED guerrero25 wrote: To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of$100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x?

1. The team purchased 200 T-shirts, sold each T-shirt for $12, and made a$900 profit.
2. In addition to the $100 setup fee, the team paid$7 for each T-shirt.

I do not have the OA with me ;i 'll update as soon as I get . Thanks in Advance .

Dear guerrero25,
This is a very tricky problem, and I'm happy to help.

First of all, here's a refresher on revenue, profit, and cost, if these ideas are rusty for you:
http://magoosh.com/gmat/2013/profit-and ... -the-gmat/

Part of what's hard is that there are two unknowns:
x = amount of discount
n = number of shirts

Statement #1: The team purchased 200 T-shirts, sold each T-shirt for $12, and made a$900 profit.
So, revenue = 200*12 = $2400. (profit) = (revenue) - (cost)$900 = $2400 - cost cost =$1500
Of that cost, $100 was for set up, so the rest is the cost of n shirts, at a rate of (8-(x/100)n), and we know n = 200$1400 = n*(8-(x/100)n) = 200*(8-(x/100)*200)
OK, this is DS. At this point, we have a single equation for x, which we could solve. This statement will allow us to solve for x.
This statement, alone and by itself, is sufficient.

Statement #2: In addition to the $100 setup fee, the team paid$7 for each T-shirt.
This tells us 7 = (8-(x/100)n)
We have to be very careful not to import information from Statement #1 here. We have a single equation with two unknowns, so we cannot solve. See:
http://magoosh.com/gmat/2012/gmat-quant ... variables/
This statement, alone and by itself, is insufficient.

It seems to me the answer is (A).

Does all this make sense?
Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Manager
Joined: 05 Jun 2012
Posts: 102
Schools: IIMA
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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30 Sep 2014, 06:47
Easy one!!!

Profit =selling price-cost

cost=(8-(x/100)*200) here n=200

selling price=200*12

profit=selling-cost price= 200*12-(8-x/2)=900 ,we have a single equation for x, which we could solve
_________________

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Senior Manager
Joined: 06 Jul 2016
Posts: 433
Location: Singapore
Concentration: Strategy, Finance
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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11 Aug 2017, 09:34
guerrero25 wrote:
To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of $100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x? Fantastic DS Question. One-time setup fee =$100
Discount per t-shirt = x cents
Price per t-shirt = $(8 - n($$\frac{x}{100}$$)) x = ? Quote: 1. The team purchased 200 T-shirts, sold each T-shirt for$12, and made a $900 profit. 2. In addition to the$100 setup fee, the team paid $7 for each T-shirt. 1) n = 200 SP =$12
=> Total Selling Price = $2400 Profit =$900
=> Cost = 2400 - 900 - 100
=> Cost = $1400 1400 = 8 - ($$\frac{x}{100}$$)*200 We can solve for x. Sufficient. 2) 7 = (8 - n($$\frac{x}{100}$$)) 2 variables and 1 equation. Insufficient. A is the answer. _________________ Put in the work, and that dream score is yours! Manager Joined: 27 Dec 2016 Posts: 233 Concentration: Social Entrepreneurship, Nonprofit GPA: 3.65 WE: Sales (Consumer Products) Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink] ### Show Tags 19 Oct 2017, 23:26 guerrero25 wrote: To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of$100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x?

1. The team purchased 200 T-shirts, sold each T-shirt for $12, and made a$900 profit.
2. In addition to the $100 setup fee, the team paid$7 for each T-shirt.

Dear expert, mikemcgarry, GMATPrepNow

I have a question about statement 2 : I think statement 2 is SUFFICIENT because of n=1. Why we don't plug n=1 in this equation, so we can get X?

Thanks!
_________________

There's an app for that - Steve Jobs.

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4677
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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20 Oct 2017, 10:47
1
KUDOS
Expert's post
septwibowo wrote:
guerrero25 wrote:
To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of $100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x? 1. The team purchased 200 T-shirts, sold each T-shirt for$12, and made a $900 profit. 2. In addition to the$100 setup fee, the team paid $7 for each T-shirt. Dear expert, mikemcgarry, GMATPrepNow I have a question about statement 2 : I think statement 2 is SUFFICIENT because of n=1. Why we don't plug n=1 in this equation, so we can get X? Thanks! Dear septwibowo, I'm happy to respond. My friend, on GMAT DS, it is absolutely crucial to be completely clear on what could be true vs. what has to be true. What could be true tells us bupkis about sufficiency. Only what has to be true tells us about sufficiency. I am not sure where you got n = 1. The problem tells us explicitly that $$n \geq 50$$, so this rules out the possibility of n = 1. Let's say n = 100, which would be possible: yes, knowing n = 100 would make the equation very easy to solve for X, but once again, our convenience and ease, in and of itself, tells us zilch about sufficiency. The prompt gives us two variables, n & x. As a very good rule of thumb, we need two separate equations to solve for the values of two variables. The GMAT loves to test this fact in word problems on the DS questions. See: GMAT Quant: How to Solve Two Equations with Two Variables Does all this make sense? Mike _________________ Mike McGarry Magoosh Test Prep Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939) Manager Joined: 27 Dec 2016 Posts: 233 Concentration: Social Entrepreneurship, Nonprofit GPA: 3.65 WE: Sales (Consumer Products) Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink] ### Show Tags 21 Oct 2017, 06:40 mikemcgarry wrote: septwibowo wrote: guerrero25 wrote: To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of$100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x?

1. The team purchased 200 T-shirts, sold each T-shirt for $12, and made a$900 profit.
2. In addition to the $100 setup fee, the team paid$7 for each T-shirt.

Dear expert, mikemcgarry, GMATPrepNow

I have a question about statement 2 : I think statement 2 is SUFFICIENT because of n=1. Why we don't plug n=1 in this equation, so we can get X?

Thanks!

Dear septwibowo,

I'm happy to respond.

My friend, on GMAT DS, it is absolutely crucial to be completely clear on what could be true vs. what has to be true. What could be true tells us bupkis about sufficiency. Only what has to be true tells us about sufficiency.

I am not sure where you got n = 1. The problem tells us explicitly that $$n \geq 50$$, so this rules out the possibility of n = 1. Let's say n = 100, which would be possible: yes, knowing n = 100 would make the equation very easy to solve for X, but once again, our convenience and ease, in and of itself, tells us zilch about sufficiency.

The prompt gives us two variables, n & x. As a very good rule of thumb, we need two separate equations to solve for the values of two variables. The GMAT loves to test this fact in word problems on the DS questions. See:
GMAT Quant: How to Solve Two Equations with Two Variables

Does all this make sense?
Mike

Thank you mikemcgarry for your explanation. I understand 100% with your explanation.

However, this is the reason why I think that n=1.

In addition to the $100 setup fee, the team paid$7 for each T-shirt.

Whatever the n shirts they buy, but if the team paid $7 for EACH means n=1 right? I buy 100 iPhone and I should pay 1.000 USD each. This is one that makes me confused. _________________ There's an app for that - Steve Jobs. Magoosh GMAT Instructor Joined: 28 Dec 2011 Posts: 4677 Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink] ### Show Tags 23 Oct 2017, 10:28 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED septwibowo wrote: Thank you mikemcgarry for your explanation. I understand 100% with your explanation. However, this is the reason why I think that n=1. In addition to the$100 setup fee, the team paid $7 for each T-shirt. Whatever the n shirts they buy, but if the team paid$7 for EACH means n=1 right?

I buy 100 iPhone and I should pay 1.000 USD each.

This is one that makes me confused.

Dear septwibowo,

I'm happy to respond.

My friend, this is a very common mistake: people often confuse the language used to express a rate for information about a total amount or number.

For example, suppose a problem says, "On Tuesday, ABC store was selling shirts at the rate of 3 shirts for $50." That "3 shirts for$50" is information about a rate, about a ratio, but this doesn't mean that the store sold exactly three shirts or only three shirts on Tuesday---that store might have sold hundreds of shirts at that price. In fact, we know that if the store sold 150 shirts that day, they would have taken in $2500 in revenue for the day. A gas station may sell gas at a rate of$3/gallon, but this doesn't mean that a driver can spend only $3 or can get only 1 gallon. This number merely give the ratio: if I put 15 gallons into my tank, that will cost me$45.

Much in the same way, this information:
the team paid $7 for each T-shirt is rate information: the word "each" does mean 1, and indeed, there's a 1 in the ratio: ($7):(1 shirt). That's the rate or ratio, but that says absolutely nothing about the total number of shirts. By contrast, n is the total number of shirts, so the total cost (not including the flat fee) would be \$7n.

Does this distinction make sense?
Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Intern
Joined: 07 Jul 2017
Posts: 10
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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29 Oct 2017, 03:25
Hello mike , I got the same doubt of septwibowo...Your explanation is very clear thanks a lot!

I think the misunderstanding is generated by wrongly interpreting the equation (8-(x/100)n). At first I thought of it as a Price*Discount*Quantity = total cost paid for the t-shirts (in this case i think septwibowo approach would have been solid). However, this equation has a totally different meaning: it puts in relation discount and total number of tshirts to give the price paid for each tshirt, therefore (8-(x/100)n) = price paid for each t shirt. In this case it becomes clear why we cannot arbitrarily consider n=1 to solve the problem.

Does it make sense? Hope this clarification, if correct, might help others with the same doubt.
Re: To raise funds, a racing team sold T-shirts imprinted with   [#permalink] 29 Oct 2017, 03:25
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