Last year, a certain company began manufacturing product X

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

Final Answer:

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

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.

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

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

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.

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.

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)

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.

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.


Cheers!!

Hi Bunuel,

How can we shortcut following tedious calculation:

\(\frac{2,000,000}{19} \approx 105,000\)

2,000,000/20 = 100,000 thus 2,000,000/19 will be a bit more.

Given:
1. Last year, a certain company began manufacturing product X and sold every unit of product X that it produced.
2. 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.
3. The company made a profit on product X last year

Asked: Did the company sell more than 21,000 units of product X last year?

Let the units of product sold by company X last year be x units and selling price be p

(1) The company's total revenue from the sale of product X last year was greater than $110,000.
Total revenues = R = xp > $110,000
Total expenses = E = $100,000 + 5%xp
Total profit = R - E = xp - ($100,000 + 5%xp) = 95%xp - $100,000 > 0
xp > (100/95) * 100,000 = $10,000,000/95
NOT SUFFICIENT

(2) For each unit of product X sold last year, the company's revenue was $5.
p = $5
Total revenues = R = 5x
Total expenses = E = $100,000 + 5%*5x
Total profit = R - E = 5x - ($100,000 + 5%*5x) = 95%*5x - $100,000 > 0
x> 10,00,000/95*5 = 21052.63 > 21000
SUFFICIENT

IMO B

Answer: Option B

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Hi Bunuel,

The question is telling that 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.

How you arrived at this equation
\(R-(100,000+0.05R)>0\) ?

It should be Expense = 100,000 + 5% of R.

Please explain what I am doing wrong.

Thanks

R = revenue.
Expenses = 100,000+0.05R

Since the company made a profit, then \(R-(100,000+0.05R)>0\).

Solution:

Question Stem Analysis:

We need to determine whether the company sold more than 21,000 units of product X last year.

Statement One Alone:

We are given that the company's total revenue from the sale of product X last year was greater than $110,000. We have a lower bound for the total revenue and we can calculate a lower bound for the total cost, but we have no information from which we can determine a lower bound for the number of units. It is possible that the company sold 25,000 units and made a revenue of $150,000 (in which case, the total cost would be 100,000 + 0.05(150,000) = $107,500), and it is possible that the company sold 20,000 units and made the same revenue. We see that the company makes a profit on product X in either case. Statement one alone is not sufficient.

Statement Two Alone:

Let the number of product X sold by the company last year be n. Since each unit generates a revenue of $5, the total revenue is 5n. We are told that the total cost is 5 percent of 5n plus $100,000; therefore the cost can be represented as 100,000 + 0.05(5n) = 100,000 + 0.25n. We are also told that the company made a profit from the sale of product X, therefore the revenue is greater than the cost. Using this information, we can create the following inequality:

5n > 100,000 + 0.25n

4.75n > 100,000

n > 100,000/4.75 ≈ 21,053

We see that n, the number of units of product X sold, is greater than 21,000. Statement two alone is sufficient.

Answer: B

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