A company's two divisions performed with remarkable consistency over

A company’s two divisions performed with remarkable consistency over the past three years:- Two divisions of a company performed very consistently over the past three years.

in each of those years, the pharmaceuticals division has accounted for roughly 20 percent of dollars sales and 40 percent of profits, and the chemicals division for the balance. - In each of the past three years,

P division accounted for 20% of dollar sales and 40% of profits

C division accounted for 80% of dollar sales and 60% of profits

When I look at these facts, one thing immediately stands out: P division generates more profits for every dollar of sales than C division.

Let me first explain what profit per dollar of sales means. In essence, it is a measure of the profitability of a company. It means that if a company generates 1 dollar of sales, how much profit does it generate? Let’s say that it generates $0.2 of profits. Its profit per dollar of sales is 0.2.

Or, if a company generates $100,000 of sales and its profits are $1000, its profit per dollar of sales is (1000/100000) 0.01.

Now, let’s understand how I can say that P division generates more profits for every dollar of sales than C division.

Let’s say that if P and C both generated the same profit for every dollar of sales, then P division should have accounted for 20% of profits. Why? Because it accounts for 20% of dollar sales, and if profit per dollar of sale is the same, then it should account for 20% of profits too.

However, P accounts for a much larger proportion of profits. Thus, P must be generating more profit for every dollar of sales than the company as a whole.

By the same logic, C division must be generating less profit per dollar of sales than the company as a whole.

Thus, P must be generating more profit per dollar of sales than C



(A)Total dollars sales for each of the company's divisions have remained roughly constant.
Incorrect- .We cannot say anything about the total dollar sales of the divisions. The total dollar sales could have increased, decreased, or remained the same. The consistency of performance is in terms of the individual divisions’ share of the company’s profits and sales, not in terms of their own sales and profits. If the company’s sales increased over the last three years, the sales of the two individual divisions also increased.

(B) The pharmaceuticals division has faced stiffer competition in its markets than has the chemicals division.
Incorrect- . This option is actually in the wrong direction. Given the facts, we understood that P division generated more profit per dollar of sales than C division. Thus, it seems rather likely that P division faced less competition than C division.

Let’s reverse the option and say:

The chemical division has faced stiffer competition in its markets than has the pharmaceutical division.

Even this option is wrong. While we know that C division had lower profit per sales than P division, we don’t know the reason for its lower profit per sales. The reason might not be stiffer competition; the reason could be lower efficiency of the C division.

(C)The chemical division has realized lower profits per dollars of sales than has the pharmaceuticals division.
Correct- . This option can be inferred, as I explained in the passage analysis.

(D) The product mix offered by each of the company's divisions has remained unchanged.
Incorrect- . The product mix might have COMPLETELY changed for the two divisions. The new products may have the same profitability (profit per sales); thus, whether the product mix has changed cannot be inferred at all from the given data about sales and profits.

(E) Highly profitable products accounted for a higher percentage of the chemicals division's sales than of the pharmaceuticals division's.
Incorrect- . This option is actually in the wrong direction. Given the facts, we understood that P division generated more profit per dollar of sales than C division. Thus, it seems reasonable to think that highly profitable products accounted for a higher percentage of the P division’s sales than of the C division’s.

So, can we infer the reverse of the option?

Can we infer the following statement?

Highly profitable products accounted for a higher percentage of the pharmaceutical division’s sales than of the chemical division’s.

No. We cannot infer (cannot be 100% sure about) this statement even though this is supported by the facts.

We cannot infer this changed option because it’s possible that highly profitable products account for the same or even lower percentage of the P division’s sales as of the C divisions’ sales.

You may wonder, “how then can P division’s profits be higher than C division’s”?

It’s possible that P’s highly profitable products are much more profitable than C division’s highly profitable products, and thus, even though they may account for the same proportion of P division’s sales, they lead to higher overall profitability of the P division.

(If you find any spelling or grammatical errors, please feel free to point them out. I haven’t checked for these errors in the above solution.)

It's 'C'

For ex. let's assume total sale is 100 and total profit is 30%, which is 30.

Pharma.: Total sale 20%, which is 20 , profit is 12 (40% of 30). Profit margin is: 100*12/20 = 60%

Chem.: Total sale 80%, which is 80, profit is 18 (60% of 30). Profit margin is: 100*18/80 = 22.5%

Therefore, Chem dept. has lower profit margin than Pharma.

If "S" is sales and "P" is profit:
\(Pharma = 0.4*P/0.2*S = 2P/S\)
\(Chemic = 0.6*P/0.8*S = 3P/4S\)

Thus, the chemical division realizes a lower profit per sales than that of the Pharma. C.

This seems like such a math question. I read through all of the answer choices and read E. I thought E was the right answer but it seemed to easy then looked back at C. C is the answer for sure. Pharma: 20% of "ales" but makes up 40% of profits.

Can some one explain me the meaning of "chemicals division for the balance"

This means:

The chemicals division (accounted for) for the balance (sales and profits).
In other words, the chemicals division accounted for 80% of sales and 60% of profit.

Pharmaceuticals division has accounted for roughly 20 percent of dollar sales and 40 percent of profits, and the chemicals division for the balance. The chemical division, therefore, accounted for 80% of the sales and 60% of the profits.

Pharma -> 20% sales, 40% profits
Chemical -> 80% sales, 60% profits

Pharma -> 20% sales, 40% profits
Chemical -> 80% sales, 60% profits

Lets say the revenue was $200 and profits were $100 (I would LOVE to have that kind of profit margin in real life!)

So, Pharma has $40 (20% of $200) in sales and $40 in profit (40% of $100)
Chemical has $160 (80% of 200) in revenue and $60(60% of $100) in profit.

Profit per dollar for Pharma = $40/$40 = 1 which is > than $60/$160 for Chemical.

Clearly, chemical division realized lower profits per dollar of sales than the pharma division as stated by C.

A company's two division performed with remarkable consistency over the past three years: in each of those years, the pharmaceuticals division has accounted for roughly 20 percent of dollars sales and 40 percent of profits, and the chemicals division for the balance.

Regarding the past three years, which of the following can properly be inferred from the statement above?

A) Total dollars sales for each of the company's divisions have remianed roughly constant.
Though the word remarkable consistency and roughly constant look synonymous but without actual number we cannot state this as conclusion for three years.

B) The pharmaceuticals division has faced stiffer competition in its markets than has the chemicals division.
We can state this. Competition to another person might be in terms of production or other factors and not sales.

C)The chemical division has realized lower profits per dollars of sales than has the pharmaceuticals division.
So if there is 100$ sales and 50$ prodit. So Pharma had 20$ sales and $8 profit. So 8/20 is the profit per dollar. Chemical has $80 sale $30 profit, so 30/80 which is lower.

D)The product mix offered by each of the company's divisions has remained unchanged.
Out of scope

E) Highly profitable products accounted for a higher percentage of the chemicals division's sales than of the pharmaceuticals division's.
We do not know about the products.

The given statement states that a company's two divisions have performed consistently over the past three years, with the pharmaceuticals division accounting for roughly 20 percent of dollar sales and 40 percent of profits, while the chemicals division accounted for the balance. Let's evaluate each option to determine which can be properly inferred from the statement:

(A) Total dollars sales for each of the company's divisions have remained roughly constant.
This cannot be properly inferred from the statement. While it provides information about the percentage of dollar sales attributed to each division, it does not indicate whether the total dollar sales for each division have remained constant or changed over the past three years.

(B) The pharmaceuticals division has faced stiffer competition in its markets than the chemicals division.
This cannot be properly inferred from the statement. The statement only provides information about the percentage of dollar sales and profits for each division and does not provide any direct indication of the level of competition faced by either division.

(C) The chemical division has realized lower profits per dollar of sales than the pharmaceuticals division.
This can be properly inferred from the statement. It mentions that the pharmaceuticals division accounted for roughly 20 percent of dollar sales and 40 percent of profits, while the chemicals division accounted for the balance. Since the pharmaceuticals division's share of profits is double its share of dollar sales, it suggests that the chemical division has realized lower profits per dollar of sales compared to the pharmaceuticals division.

(D) The product mix offered by each of the company's divisions has remained unchanged.
This cannot be properly inferred from the statement. While the statement provides information about the percentage of dollar sales and profits for each division, it does not provide any details about the specific products or their mix offered by each division, making it impossible to determine if the product mix has remained constant or changed.

(E) Highly profitable products accounted for a higher percentage of the chemicals division's sales than of the pharmaceuticals division's.
This cannot be properly inferred from the statement. It provides information about the percentage of dollar sales and profits for each division but does not provide any details about the profitability of specific products or whether highly profitable products accounted for a higher percentage of sales in either division.

In conclusion, based on the given statement, the only inference that can be properly made is that the chemical division has realized lower profits per dollar of sales compared to the pharmaceuticals division (option C). The statement's information about the pharmaceuticals division accounting for a higher share of profits than its share of dollar sales suggests that it has a higher profitability per dollar of sales compared to the chemical division. The other options either lack sufficient evidence or go beyond the information provided in the statement.