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Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

(1) The company's total revenue from the sale of product X last year was greater than $110,000.
(2) For each unit of product X sold last year, the company's revenue was $5.
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New post 14 Dec 2012, 07:20
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Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

Since the company made a profit, then \(R-(100,000+0.05R)>0\) --> \(R>(\frac{2,000,000}{19} \approx 105,000)\).

(1) The company's total revenue from the sale of product X last year was greater than $110,000 --> \(R > 110,000\). It's possible that company sold just one unit for say $120,000 or 120,000 units for $1. Not sufficient.

(2) For each unit of product X sold last year, the company's revenue was $5. If total of n units were sold, then the total revenue would be $5n, so R = 5n --> \(5n>\frac{2,000,000}{19}\) --> \(n>\frac{400,000}{19}>21,000\). Sufficient.

Answer: B.
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 17 Jul 2013, 12:39
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Statement 1: Top line revenue numbers only. Doesn't tell us anything about unit costs or information helping us to figure out how many units need to be sold. Not sufficient.

Statement 2: Assume that they sold 21000 units with $5 revenue per unit. This leaves us with $105 000 total revenue. The expenses would then be $100 000 + 5% of $105 000 = $105 250. This would lead to a loss not a profit so the company MUST have sold more than 21000 units to be profitable.

Answer B.
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New post 16 Jul 2013, 18:35
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Bunuel wrote:
Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

Since the company made a profit, then R-(100,000+0.05R)>0 --> R>2,000,000/19=~105,000.

(1) The company's total revenue from the sale of product X last year was greater than $110,000 --> R>110,000. Its possible that company sold just one unit for say $120,000 or 120,000 units for $1. Not sufficient.

(2) For each unit of product X sold last year, the company's revenue was $5. If total of n units were sold, then the total revenue would be $5n, so R=5n --> 5n>2,000,000/19 --> n>400,00/19>21,000. Sufficient.

Answer: B.



I understand how you came up with R-(100,000+0.05R)>0 but how did you go about creating the equation R>2,000,000/19=~105,000.

Thanks
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 16 Jul 2013, 22:04
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hfbamafan wrote:
Bunuel wrote:
Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

Since the company made a profit, then R-(100,000+0.05R)>0 --> R>2,000,000/19=~105,000.

(1) The company's total revenue from the sale of product X last year was greater than $110,000 --> R>110,000. Its possible that company sold just one unit for say $120,000 or 120,000 units for $1. Not sufficient.

(2) For each unit of product X sold last year, the company's revenue was $5. If total of n units were sold, then the total revenue would be $5n, so R=5n --> 5n>2,000,000/19 --> n>400,00/19>21,000. Sufficient.

Answer: B.



I understand how you came up with R-(100,000+0.05R)>0 but how did you go about creating the equation R>2,000,000/19=~105,000.

Thanks


Step by step simplificatio:

\(R-(100,000+0.05R)>0\)

\(R-100,000-0.05R>0\)

\(0.95R-100,000>0\)

\(\frac{19R}{20}-100,000>0\)

\(\frac{19R}{20}>100,000\)

\(R>\frac{2,000,000}{19}\)

Hope it's clear.
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 01 Dec 2013, 06:19
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In case someone ends up having an issue with the same question and wants to avoid dividing by 19

A is not sufficient as unit item can 1 or 21000

B
let N be the number sold which implies total sales is 5N

5N - (100,000+(.05)*5N) > 0
5N - 100k - .05N >

475N> 10,000,000
N>200000/9 which is approx 22.2k

hence sufficient
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 18 May 2014, 09:47
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Statement 1: The company's total revenue from the sale of product X last year was greater than $110,000.
No way to determine the number of units sold.
INSUFFICIENT.

Statement 2: For each unit of product X sold last year, the company's revenue was $5.
Plug in the THRESHOLD of 21,000 units:
Total revenue = 5(21,000) = 105,000.
Total expenses = 100,000 + .05(105,000) = 105,250.
Not possible, since the company must make a profit.
Test a GREATER number of units: 100,000.
Total revenue = 5(100,000) = 500,000.
Total expenses = 100,000 + .05(500,000) = 125,000.
Here, the company makes a profit.
Thus, to make a profit, the company must sell MORE than 21,000 units.
SUFFICIENT.

The correct answer is B.
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 18 Jan 2015, 04:03
RustyR wrote:
Bunuel wrote:
[b] n>400,00/19>21,000. Sufficient.

Answer: B.


How should we go about solving 400,00/19 in timed conditions?



No need to solve it, since you know that there is a profit and you know the average revenue you can figure out minimum number of units sold to make that profit.
its a DS question so no need to solve
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 21 May 2015, 06:32
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Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

My Approach:

Let price of each product be P$ and N be the number of units sold by the company last year.

What is provided to us:: (N*P) - (100,000 + (.05)N*P) > 0 --- [company made a profit on product X last year]

=> (.95)N*P - 100,000 > 0.

=> N*P > 100,000/.95

Now, We need to find whether N > 21,000 or Not!
So we have to look for a condition which would either straight away give us value of N or value of P so that we can determine the value of N.

(1)- The company's total revenue from the sale of product X last year was greater than $110,000.

==> N*P > 110,000 -- Already we have one such inequality. This does not help, neither we get to know the value of N nor the value of P.

Hence, Insufficient.


(2)- For each unit of product X sold last year, the company's revenue was $5.

==>So, P = 5; We can Clearly find the value of N now.

==> N*5 > 100,000/(.95) => N > 1,00,00,000/(95*5) => N > 400,000/19 => N > 21,000

Hence, Sufficient.

Ans:: B.
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 21 May 2015, 10:37
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Hi All,

GMAT questions are always carefully worded - the numbers involved are NEVER random and the questions asked are specifically-worded for a reason. As such, you can take advantage of those patterns when working through Quant questions.

Here, we're told a number of facts about a company:
1) It sold EVERY unit of product X that it produced.
2) Total expenses were $100,000 + 5% of revenue from those sales.
3) The company made a PROFIT on these sales.

The question asks if the company sold MORE than 21,000 units of product X. This is a YES/NO question.

Before dealing with the two Facts, notice that the expenses were MORE than $100,000 (since the revenue factors in to that calculation), but we know that the company made a PROFIT. That combination of facts will come in handy in just a moment....

Fact 1: Total revenue from product X was GREATER than $110,000

This confirms something that we already knew (the company made a profit), but we don't know how many units were sold to earn that revenue.
Fact 1 is INSUFFICIENT

Fact 2: Each unit of Product X sold brought in $5 of revenue.

Since the question asks specifically if MORE than 21,000 units were sold, we can use this number as a 'gauge'....

IF....
21,000 units were sold at $5 per unit, we'd have 21,000(5) = $105,000 of revenue

We were told that the EXPENSES = $100,000 + 5% of revenue.....

5% of $105,000 = $5,250
$100,000 + $5,250 = $105,250
In this scenario, the expenses are GREATER than the revenue....
BUT we were told that the company made a PROFIT, so this CANNOT be what happened. If only 21,000 units were sold at this price, then the company would NOT have been profitable. Thus, MORE than 21,000 units would have to have been sold.
Fact 2 is SUFFICIENT

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Last year, a certain company began manufacturing product X a  [#permalink]

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New post 11 Nov 2015, 04:26
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sambam wrote:
Statement 1: Top line revenue numbers only. Doesn't tell us anything about unit costs or information helping us to figure out how many units need to be sold. Not sufficient.

Statement 2: Assume that they sold 21000 units with $5 revenue per unit. This leaves us with $105 000 total revenue. The expenses would then be $100 000 + 5% of $105 000 = $105 250. This would lead to a loss not a profit so the company MUST have sold more than 21000 units to be profitable.

Answer B.


Great solution +1. I would add, that we already know from the text that the Revenue > ~105000 (20/19*100000 ~ 105263), hence if we use the min value of 21000*5=105000, there must be > 21000 units.
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New post 25 Nov 2015, 07:05
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Here is almost no calculation approach:

St1: clearly insufficient it could be just 1 heavy m/c or 110,000 widgets sold.
St2: The stimulus says the company made profit i.e. broke even. Thus it should produce at least 100000/0.95P units. (P=5=selling price of X) If we know that 100,000/.95P>21000 SUFF and if 100,000/.95P<21000 INSUFF

100,000/.95*5>21,000?
400/19>21?
400>21*19? We know this is true as 21*19 will always be less than 20*20=400( PS: 9*11<10*10, 4*6<5*5 etc I think you get the idea)

Special Note: For problems related to break even analysis one of the most important formula to remember is: No of Units= Total Fixed Cost/Per Unit Profit. Most of the GMAT problem on this topic will play around this formula.
For break even analysis pls check - https://en.wikipedia.org/wiki/Break-even_(economics)
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 26 Nov 2015, 07:15
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

(1) The company's total revenue from the sale of product X last year was greater than $110,000.
(2) For each unit of product X sold last year, the company's revenue was $5.

There are 2 variables (p: selling unit price, n; selling products' number) and 2 equations are given by the 2 conditions
Looking at the conditions together, 110,000/5=22,000>21,000, so this answers the question 'yes' and (C) seems like the answer. However, the number of the product is a hidden integer, so if we apply commonly made mistakes type 4(A),
For condition 1, even if the total sales is $110,000, we cannot know the number of cars, as if the price of one car is $110,000, it is 'no' but 'yes' when the price of a bolt is $1.
For condition 2, 100,000+5n(0.05)<5n --> 100,000<4.75n, 100,000/4.75<n, 21,052<n. This is sufficient and the answer becomes (B).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 07 Dec 2015, 07:19
Simple logic: revenue must exceed the manufacturing expenses. In part B, if we consider 21000 units at 5$ profit for each unit then the total revenue is 105000$, which will be less than the manufacturing expenses(105250$) so this means that the manufacturing company must have sold more than 21000 units to achieve profitability as mentioned in the question.

Therefore B is sufficient.


For part A , I agree with Bunuel. Total revenue is given. This revenue can be made by selling n products and n can be anything.

Therefore A is not sufficient.


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Last year, a certain company began manufacturing product X a  [#permalink]

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New post 13 Aug 2016, 05:30
Let X = No of items sold
Y = Revenue per item

R = X Y

Given R - 100000 -0.05 R > 0
0.95 XY - 100000>0

Let company sold 21k units ,

Y > 100000/(0.95 * 21000) ~~ app = 5

A) Insufficient -- as it does not provide any information regarding Rev/Item
B) It provides info regarding Rev/item ----> Sufficient
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 13 Aug 2016, 23:52
Walkabout wrote:
Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

(1) The company's total revenue from the sale of product X last year was greater than $110,000.
(2) For each unit of product X sold last year, the company's revenue was $5.


We know, profit = Revenue- expenses.

it is given that profit > 0.

Hence, Revenue > Expenses.

Now Expenses = 100000 + 5% of R

or E = 100000 + 1/20R

==> R > 100000 + 1/20R

or 19/20 R > 100000

or R > (20/19) *100000

Now, as per A, we are given R >110000 but we don't know the price of one unit. Hence, we cannot determine number of units.

As per B, we have R = 5*n , where n is number of units.

or 5*n > (20/19) *100000

or n>21000. Hence Sufficient. Answer is B.
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 22 Mar 2018, 18:38
Walkabout wrote:
Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

(1) The company's total revenue from the sale of product X last year was greater than $110,000.
(2) For each unit of product X sold last year, the company's revenue was $5.


Sol.

Revenue = Price (P) * Quantity (Q)
Revenue has to be bigger to the costs to make a profit:
PQ > 100,000+5%PQ
95%PQ > 100,000

If we asume that they sold 21,000 units then we look for the Min Price to get a profit selling 21,000 units

95%P(21,000) > 100,000
P > 100,000/(95%*21,000)
P > 5.0125 (Just notice that is more than 5). So they would have to sell more than 21,000 units in order to make some profit. Suff
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 12 Jun 2018, 18:38
Hi,

Could anybody please explain me a way to effectively check whether R>2,000,000/19 is more than 21,000? It does seem to be higher than 20,000, but in the heat of a moment I may have a doubt and think that this might be a trap because the number could be very close to 21,000.

Thank you guys
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 03 Sep 2018, 08:19
Hi Bunuel

How can we shortcut the following calculation:

2,0000,000 / 19 = approximately 105,000

Thank you for your time.
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 03 Sep 2018, 08:22
Bunuel wrote:
Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

Since the company made a profit, then \(R-(100,000+0.05R)>0\) --> \(R>(\frac{2,000,000}{19} \approx 105,000)\).

(1) The company's total revenue from the sale of product X last year was greater than $110,000 --> \(R > 110,000\). It's possible that company sold just one unit for say $120,000 or 120,000 units for $1. Not sufficient.

(2) For each unit of product X sold last year, the company's revenue was $5. If total of n units were sold, then the total revenue would be $5n, so R = 5n --> \(5n>\frac{2,000,000}{19}\) --> \(n>\frac{400,000}{19}>21,000\). Sufficient.

Answer: B.


Hi Bunuel,

How can we shortcut following tedious calculation:

\(\frac{2,000,000}{19} \approx 105,000\)
GMAT Club Bot
Re: Last year, a certain company began manufacturing product X a &nbs [#permalink] 03 Sep 2018, 08:22

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