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Last year, a certain company began manufacturing product X a

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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, 23:57
FANewJersey 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 \(R-(100,000+0.05R)>0\) --> \(R>(\frac{2,000,000}{19} \approx 105,000)\).

(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:

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


2,000,000/20 = 100,000 thus 2,000,000/19 will be a bit more.
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Re: Last year, a certain company began manufacturing product X a  [#permalink]

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New post 04 Sep 2018, 00:16
Only if the company made more than 21000 products n sold for 5 dollar each, it would have made a profit.

Since the total cp is 105250 and revenue for 21000 is 105000


Where as statement A is irrelevant and doesn't give any info on the total revenue or no. Of products. And is not needed in anyway to support statement B.


Hence answer B

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

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New post 29 Jul 2019, 07:19
In this question,

I arrived at the equation from question statement -->
R > 20,00,000/19

Now, instead of solving, I converted R = xp (where x is units and p is price or revenue per unit).

Hence, the equation becomes xp > 2000000/19

Now, the question asks did the company sell more than 21,000 units of product X last year ==> Is x>21000 ?

This can be answered if we know the value of p.

Statement B gives us the value of p. The point is, we don't even need to solve the equations. We just need to know if this info is sufficient to give us a definite yes or no.

Please correct me if I'm wrong Bunuel chetan2u

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

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New post 19 Sep 2019, 01:38
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.


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

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New post 15 Oct 2019, 20:41
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.

Bunuel
How do we know
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
is total cost price or per unit cost price
the company's total expenses for manufacturing product X : so it may be interpreted as cost for manufactring one product.What will be the language if it is per product cost?
Plz clear this
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Last year, a certain company began manufacturing product X a   [#permalink] 15 Oct 2019, 20:41

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