Last visit was: 21 Jul 2024, 22:42 It is currently 21 Jul 2024, 22:42
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 10 Apr 2012
Posts: 244
Own Kudos [?]: 4550 [55]
Given Kudos: 325
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE:Project Management (Telecommunications)
Send PM
Most Helpful Reply
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28861 [10]
Given Kudos: 130
General Discussion
User avatar
Intern
Intern
Joined: 05 Jun 2012
Posts: 33
Own Kudos [?]: 55 [0]
Given Kudos: 66
Schools: IIMA
Send PM
Senior Manager
Senior Manager
Joined: 06 Jul 2016
Posts: 277
Own Kudos [?]: 378 [1]
Given Kudos: 99
Location: Singapore
Concentration: Strategy, Finance
Send PM
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
1
Bookmarks
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.
Manager
Manager
Joined: 27 Dec 2016
Posts: 195
Own Kudos [?]: 185 [0]
Given Kudos: 285
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE:Marketing (Education)
Send PM
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
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!
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28861 [1]
Given Kudos: 130
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
1
Kudos
Expert Reply
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 :-)
Manager
Manager
Joined: 27 Dec 2016
Posts: 195
Own Kudos [?]: 185 [0]
Given Kudos: 285
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE:Marketing (Education)
Send PM
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
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.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28861 [3]
Given Kudos: 130
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
2
Kudos
1
Bookmarks
Expert Reply
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 :-)
Intern
Intern
Joined: 07 Jul 2017
Posts: 7
Own Kudos [?]: 3 [0]
Given Kudos: 14
Send PM
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
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.
Director
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 235 [0]
Given Kudos: 432
Location: United States
Send PM
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
In statement 2, we don't know the value of the discount. Based on the statement, we can only conclude that after the t-shirt was discounted, the team paid $7 per shirt.

We can make the following equation provided by the information in statement 2:

\(7 = (8-\frac{x}{100}n)\) dollars

However, without knowing what n is, we can't determine the value of x. If n = 50, then x = 2. If n = 100, then x = 1.

\(7 = (8-\frac{2}{100}50)\) dollars

\(7 = (8-\frac{1}{100}100)\) dollars

We can't determine the value of x cents based off statement 2 alone.
Intern
Intern
Joined: 14 May 2023
Posts: 11
Own Kudos [?]: 8 [0]
Given Kudos: 44
Location: India
GMAT 1: 740 Q49 V41
GPA: 3.4
Send PM
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
Basshead wrote:
In statement 2, we don't know the value of the discount. Based on the statement, we can only conclude that after the t-shirt was discounted, the team paid $7 per shirt.

We can make the following equation provided by the information in statement 2:

\(7 = (8-\frac{x}{100}n)\) dollars

However, without knowing what n is, we can't determine the value of x. If n = 50, then x = 2. If n = 100, then x = 1.

\(7 = (8-\frac{2}{100}50)\) dollars

\(7 = (8-\frac{1}{100}100)\) dollars

We can't determine the value of x cents based off statement 2 alone.


Doesn't n stand for the number of shirts?

So in statement 2, if we substitute n with 1, we get 7 = 1*( 8 - x/100) => x=100?

What's wrong with this?
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34042
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
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.
GMAT Club Bot
Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]
Moderator:
Math Expert
94441 posts