Store A and Store B in a residential complex supply eggs in cartons of

Question

Store A and Store B in a residential complex supply eggs in cartons of two sizes: six-egg cartons and twelve-egg cartons. Both stores charge the same amount of money for each six-egg carton, and both charge the same amount for each twelve-egg carton. Both stores have a smaller per-egg profit margin for twelve-egg cartons compared to the margin for six-egg cartons. In a certain month, the total profits from egg sales were the same for the two stores. Which store sold more eggs in that month?

(1) In that month, the proportion of twelve-egg cartons sold in relation to six-egg cartons sold was greater for Store B than for Store A.
(2) In that month, both stores sold about the same number of cartons of eggs.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Bunuel · Accepted Answer

Store A and Store B in a residential complex supply eggs in cartons of two sizes: six-egg cartons and twelve-egg cartons. Both stores charge the same amount of money for each six-egg carton, and both charge the same amount for each twelve-egg carton. Both stores have a smaller per-egg profit margin for twelve-egg cartons compared to the margin for six-egg cartons. In a certain month, the total profits from egg sales were the same for the two stores. Which store sold more eggs in that month?

We are given that:

• the profit per egg is higher for six-egg cartons than for twelve-egg cartons.
• for a certain month, the total profits from egg sales were the same for the two stores.

The question asks which store sold more eggs in that month.

For fixed total profit and fixed profit per egg for each type of carton, the store with a higher proportion of twelve-egg cartons must sell more eggs overall. Intuitively, twelve-egg cartons bring less profit per egg, so a store that relies more on twelve-egg cartons must move more total eggs to reach the same total profit.

(1) In that month, the proportion of twelve-egg cartons sold in relation to six-egg cartons sold was greater for Store B than for Store A.

This means Store B’s mix is more heavily weighted toward the lower-margin twelve-egg cartons. Its average profit per egg is therefore lower than Store A’s. Since total profit is the same for both stores, the only way for Store B to match Store A’s profit with a lower profit per egg is to sell more eggs. So Store B sold more eggs. Sufficient.

(2) In that month, both stores sold about the same number of cartons of eggs.

This is vague. Even if we interpret it as “the same total number of cartons,” it still does not tell us how many of those cartons were six-egg versus twelve-egg for each store. You can construct scenarios consistent with the stem and statement (2) where Store A sells more eggs and others where Store B sells more eggs. Not sufficient.

Answer: A.

Tucky · Answer

I got this right during mock, assuming that Profit per egg of 6-carton egg is same for Store-A and Store-B, and the same for 12-carton egg.

But now during the review, i ain't sure whether my assumption was correct, and i am not sure whether question hints us towards this end.

Would love some help here.

afluck29 · Answer

I did the same and it worked, so I assume you should do it like this

Tucky · Answer

Bunuel , My doubt was: how did we infer the bold highlighted   fixed profit per egg  ? did you assume or question hints us towards that end? The question just says that:  Both stores charge the same amount of money for each six-egg carton, and both charge the same amount for each twelve-egg carton.

Maybe for 
 Store A:  Profit/12-egg carton = 3, Profit/6-egg carton = 20
for  Store B:  Profit/12-egg carton = 10, Profit/6-egg carton = 50

And accordingly, we can take nos, which can provide inconclusive answers

Bunuel · Answer

You are misunderstanding the phrase “both stores charge the same amount.”

It means the  price per 6-carton is the same for both stores  and the  price per 12-carton is the same for both stores .

yzhou0523 · Answer

Yes, even though both stores charge the same amount—for example, 100 for a six-egg carton and 200 for a twelve-egg carton—we can still have cases like:
 Store A:  Profit/12-egg carton = 3, Profit/6-egg carton = 20
for  Store B:  Profit/12-egg carton = 10, Profit/6-egg carton = 50

kartickdey · Answer

Bunuel   KarishmaB  
Instead of explaining it in language, Will anyone please explain it mathematically?

kartickdey · Answer

I think in the explanation you have assumed that the Cost price of eggs for both the store is same but nowhere it is mentioned.

MartyMurray · Answer

The question is busted. Without the relationships between the two stores' profit margins per egg in the two types of cartons, there's no way to answer the question.

Store A and Store B in a residential complex supply eggs in cartons of

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Store A and Store B in a residential complex supply eggs in cartons of

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