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A garden center sells a certain grass seed in 5-pound bags

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A garden center sells a certain grass seed in 5-pound bags

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Source: Official Guide

A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags at $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?

A. $94.03
B. $96.75
C. $98.78
D. $102.07
E. $105.3

The OA is B.

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BTGmoderatorLU wrote:
Source: Official Guide

A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags at $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?

A. $94.03
B. $96.75
C. $98.78
D. $102.07
E. $105.3
5-pound bags = ($13.85)/5 ≈ $3 per pound.
10-pound bags = ($20.43)/10 = more than $2 per pound.
25-pound bags = ($32.25)/25 = less than $1.50 per pound.

To minimize the cost, we must maximize the number of 25-pound bags, which offer seed at the lowest price per pound.
Two 25-pound bags = 50 pounds = (2)(32.25) = $64.50.
To bring the weight to between 65 and 80 pounds, inclusive, we must buy at least 15 more pounds.
It is cheaper to buy one more 25-pound bag ($32.25) than to buy one 10-pound bag and one 5-pound bag (more than $33).
Adding $32.25 to the value in blue, we get:
64.50 + 32.25 = $96.75.

The correct answer is B.

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BTGmoderatorLU wrote:
Source: Official Guide

A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags at $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?

A. $94.03
B. $96.75
C. $98.78
D. $102.07
E. $105.3

The OA is B.
The prices are based on the concept of the more one buys, the less per unit price one pays.

Let's first confirm this.

1. 5-pound bags at $13.85 per bag => 13.85/5 = 2.77/lbs
2. 10-pound bags at $20.43 per bag => 20.43/10 = 2.043/lbs
3. 25-pound bags at $32.25 per bag=> 32.25/25 = 1.29/lbs

We are given that 65 ≤ Quantity bought ≤ 80

Since the price per lbs is least for the 25-pound bag, we must buy two bags, this will make 50-pounds = 2*32.25 = $64.50

Now we need at least 65 - 50 = 15 pounds

Case 1: Buying one 5-pound bag and one 10-pound bag; they will cost = 13.85 + 20.43 = $34.28

Total cost of 65 pounds of seeds = 64.50 + 34.28 = $98.78

Case 2: Buying one more 25-pound bag; it will cost = 32.25

Total cost of 65 pounds of seeds = 64.50 + 32.25 = $96.75 < $98.78

The correct answer: B

Hope this helps!

-Jay
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Hi All,

We're told that a garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags at $32.25 per bag. We're asked, if a customer is to buy AT LEAST 65 pounds of the grass seed, but NO MORE THAN 80 pounds, what is the least possible cost of the grass seed that the customer could buy. This question is really just about basic Arithmetic, but you have to be careful about answering the question that is ASKED.

Many Test Takers would focus on buying exactly 65 pounds of seed (with one 5-pound bag, one 10-pound bag and two 25-pound bags). This would lead to Answer C. However, the question did NOT ask for the cost of 65 pounds of seed; it asked for the LEAST amount you could spend while buying "AT LEAST 65 pounds... but NO MORE THAN 80 pounds." That wording should make you consider whether you've actually spent the LEAST amount possible or not (and whether you should be focused on 65 pounds or some other total...)....

With a quick comparison of the three prices, you should notice that 10-pound bag costs LESS than two 5-pound bags and a 25-pound bag costs LESS than two 10-pound bags. Thus, the lowest price-per-pound occurs when we buy 25-pound bags of seed.

To hit 65 pounds exactly, we have to buy 4 bags (including 2 that are more costly per pound). With 75 pounds though, we can buy just 3 of the 25-pound bags - and get the LOWEST price-per-pound. That total would be 75 pounds and cost (3)($32.25) = $96.75. THAT is the actual lowest price possible.

Final Answer: B

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

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Contact Rich at Rich.C@empowergmat.com

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BTGmoderatorLU wrote:
Source: Official Guide

A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags at $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?

A. $94.03
B. $96.75
C. $98.78
D. $102.07
E. $105.3
The per-pound cost of the 5-pound bag is 13.85/5 = $2.77. The per-pound cost of the 10-pound bag is 20.43/10 = $2.043. The per-pound cost of the 25-pound bag is 32.25/25 = $1.29. Since the 25-pound bag has the least per-pound cost and we see that if the customer buys three 25-pound bags, he will have 75 pounds of grass seed, which is more than 65 pounds but less than 80 pounds. The cost of three such bags is 3 x 32.25 = $96.75.

One might argue that he can buy 2 bags of 25 pounds, 1 bag of 10 pounds and 1 bag of pounds of grass seed, which satisfies the minimum of 65 pounds of grass seed. However, the cost of such a purchase would be 2 x 32.25 + 20.43 + 13.85 = $98.78, which is more than $96.75.

Answer: B

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Scott Woodbury-Stewart Founder and CEO

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