A rectangular garden that is 10 feet long and 5 feet

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

A rectangular garden that is 10 feet long and 5 feet

by Vincen » Wed Feb 21, 2018 2:22 am

A rectangular garden that is 10 feet long and 5 feet wide is to be covered with a layer of mulch 0.5 foot deep. At which store, K or L, will the cost of the necessary amount of mulch be less?

(1) Store K sells mulch only in bags, each of which costs $7 and contains 6.25 cubic feet of mulch.
(2) Store L sells mulch only in bags, each of which costs $40 and contains 25 cubic feet of mulch.

Are both statements sufficient? How can I show it? Experts, can you help me here? Thanks in advanced.

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Source: Beat The GMAT — Data Sufficiency | Wed Feb 21, 2018 2:22 am

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 am; Thanked: 86 times; Followed by:15 members; GMAT Score:770

by ErikaPrepScholar » Wed Feb 21, 2018 8:43 am

Using the question stem, we should be able to solve for the volume of mulch that we need (10ft * 5ft * 0.5ft = 25ft^3). We want to find which store will allow us to buy enough mulch at the lowest price. This means we need to know both 1) how many bags of mulch we need at each store and 2) how much a bag of mulch costs at each store.

Looking at the answer choices, we should see that from Statement 1, we can figure out 1) how many bags of mulch we need at Store K and 2) how much a bag of mulch costs at store K. However, we know nothing about Store L! So this is insufficient. For Statement 2, we can figure out 1) how many bags of mulch we need at Store L and 2) how much a bag of mulch costs at store L, but we know nothing about Store K! So this is also insufficient. Together, these two statements tell us 1) how many bags of mulch we need at each store and 2) how much a bag of mulch costs at each store, so they should be sufficient together, making answer choice C correct.

We don't need to do any math to prove that C is the correct answer, but if we did, it would look like this:

Statement 1:
We need 25ft^3 of mulch. Each bag at Store L is 6.25ft^3. If we buy 4 bags of mulch, we will have exactly 25ft^3 of mulch. Each bag costs $7, so 4 bags should cost 4*7 = $28. So we'll need to spend $28 at Store L.

Statement 2:
Each bag at Store K is 25ft^3. If we buy 1 bag of mulch, we will have exactly the amount we need. Each bag costs $40, so we'll need to spend $40 at Store K.

Note: while buying bags of mulch got us exactly the amount of mulch we need at both stores, on more complicated problems, we'll end up needing to buy a final bag of mulch that we won't need all of. Remember that when we end up with a fraction of a unit that we can't take a fraction of (like a bag of mulch), we always need to round up to ensure that we get the full amount we need.