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A garden center sells a certain grass seed in 5pound bags at $13.85
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03 Jul 2016, 11:17
Question Stats:
68% (02:19) correct 32% (02:29) wrong based on 1170 sessions
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A garden center sells a certain grass seed in 5pound bags at $13.85 per bag, 10pound bags at $20.43 per bag, and 25pound bags $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
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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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29 Jun 2018, 21:12
adkikani wrote: niks18 chetan2u gmatbusters pushpitkc pikolo2510Quote: A garden center sells a certain grass seed in 5pound bags at $13.85 per bag, 10pound bags at $20.43 per bag, and 25pound bags $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? I was not able to understand below quote by Skywalker18Quote: As it is evident that 25 pound bag gives the least possible cost of the grass . Is it required to take a ratio of price by weight ? Are we working on LCM / approximation in this Q? As per Q stem, we are only given a range of weight by which gardener sells grass seed. the average price is the least when bought in 25 pound bags.. avg price per pound 1) 25 pound bag = 32.25/25 = 1.29 per pound 2) 10 pound bag = 20.43/10 = 2.043 3) 5 pound bag = 13.85/5=2.77 so 25 pound bag are the best to reduce cost but 65 requires other bags to as 65 is not a multiple of 25
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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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03 Jul 2016, 11:31
As it is evident that 25 pound bag gives the least possible cost of the grass . So , we should maximize the number of 25 pound bags . Since , the customer should buy at least 65 pounds and at most 80 pounds . Therefore , the customer should buy 25*3 = 75 pounds . Since , the customer can satisfy the weight requirement using the 25 pound bag , he need not buy any other bag size Least possible cost of grass seed that customer will buy = 32.25 * 3 = 96.75 $ Answer B
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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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04 Jul 2016, 00:09
there can be 2 cases
1)25+25+10+5=$98.78 or 2)25+25+25=$96.75
2 one is less amount and satisfies criteria between 6580.if there are more cases it will obviously be more than $100



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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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04 Jan 2018, 01:01
Any mechanism to solve it other than brute force?



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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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08 Apr 2018, 12:47
Bunuel Is there a quick method to solve the problem ? It took a bit extra time to calculate please help
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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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08 Apr 2018, 13:47
chandan1988, see if it helps: In terms of the weight of bags, we could write the following equation: 65 <= 5*a + 10*b + 25*c <= 80 or 13 <= a + 2*b + 5*c <= 80 (equation I) In terms of the total cost (T) we could write: 13.85*a + 20.43*b + 32.33*c = T, for which we want to minimize the value of T. The main problem is that we have (a, 2b, 5c) in the first equation, and (a, b, c) in the second. But, what if we just transform the variables in the second equation to (a, 2b, 5c)? T = 13.85*a + (20.43/2)*(2b) + (32.25/5)*(5c) = 13.82*a + 10.215*(2b) + 6.45*(5c) (equation II) Thus, now we have a system of two equations, for which is clear that best thing to do is maximize c. In other words, to solve it more quickly, we must think what kind of bag is the cheapest in terms of $ per pound.



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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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19 May 2018, 15:49
Bunuel wrote: A garden center sells a certain grass seed in 5pound bags at $13.85 per bag, 10pound bags at $20.43 per bag, and 25pound bags $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 This is a straight forward question with a straightforward method to solve. However, a lot of time gets eaten up while solving and eliminating wrong answers. What timeefficient method do you suggest solving this problem? Or is the key simply to recognize 25 lb. bags gives us the "most bang for our buck" before we start our calculations, so we should know to solve for as much 25 lb. bags needed to meet the weight requirement? (i hope my question makes sense)



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A garden center sells a certain grass seed in 5pound bags at $13.85
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29 Jun 2018, 21:00
niks18 chetan2u gmatbusters pushpitkc pikolo2510Quote: A garden center sells a certain grass seed in 5pound bags at $13.85 per bag, 10pound bags at $20.43 per bag, and 25pound bags $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? I was not able to understand below quote by Skywalker18Quote: As it is evident that 25 pound bag gives the least possible cost of the grass . Is it required to take a ratio of price by weight ? Are we working on LCM / approximation in this Q? As per Q stem, we are only given a range of weight by which gardener sells grass seed.
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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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02 Oct 2018, 21:22
Hi All, We're told that a garden center sells a certain grass seed in 5pound bags at $13.85 per bag, 10pound bags at $20.43 per bag, and 25pound 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 5pound bag, one 10pound bag and two 25pound 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 10pound bag costs LESS than two 5pound bags and a 25pound bag costs LESS than two 10pound bags. Thus, the lowest priceperpound occurs when we buy 25pound 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 25pound bags  and get the LOWEST priceperpound. That total would be 75 pounds and cost (3)($32.25) = $96.75. THAT is the actual lowest price possible. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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03 Oct 2018, 17:56
Bunuel wrote: A garden center sells a certain grass seed in 5pound bags at $13.85 per bag, 10pound bags at $20.43 per bag, and 25pound bags $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 perpound cost of the 5pound bag is 13.85/5 = $2.77. The perpound cost of the 10pound bag is 20.43/10 = $2.043. The perpound cost of the 25pound bag is 32.25/25 = $1.29. Since the 25pound bag has the least perpound cost and we see that if the customer buys three 25pound 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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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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26 Oct 2018, 17:01
We are told at least 65 but less than 80
We are also concerned with the least amount to be paid.
So our maximum bought is 75 and minimum is 65
We know that buying 25 pounds is cheaper per pound than buying the other bags.
3 * 25 = 75 pounds. This way 3 * 32.25 = 96.75
Now the other way is for 65 pounds = 2 * 32.25 + 20.43 + 13.85 = 64.50 + 20.43 + 13.85 = 98.78
We know that buying 3 bags of the 25 pounds costs less than buying 65 pounds.
Answer choice B



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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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07 Nov 2018, 00:11
chetan2u wrote: adkikani wrote: niks18 chetan2u gmatbusters pushpitkc pikolo2510Quote: A garden center sells a certain grass seed in 5pound bags at $13.85 per bag, 10pound bags at $20.43 per bag, and 25pound bags $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? I was not able to understand below quote by Skywalker18Quote: As it is evident that 25 pound bag gives the least possible cost of the grass . Is it required to take a ratio of price by weight ? Are we working on LCM / approximation in this Q? As per Q stem, we are only given a range of weight by which gardener sells grass seed. the average price is the least when bought in 25 pound bags.. avg price per pound 1) 25 pound bag = 32.25/25 = 1.29 per pound 2) 10 pound bag = 20.43/10 = 2.043 3) 5 pound bag = 13.85/5=2.77 so 25 pound bag are the best to reduce cost but 65 requires other bags to as 65 is not a multiple of 25 Hi Chetu Thanks, I used similar approach and got the correct answer. Just wanted to check, because we can also buy atmost 80 pounds, we could have bought 3 of 25 pound bag and 1 bag of 5 pound, which comes to 96.75 + 13.85 ( 5 pound bag cost ).\ = 110 approx. Because my answer was not there, I chose 96.75. Is my approach correct ?



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Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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17 Jan 2019, 19:42
I have a process that will save you some time from brute forcing.
First, You must recognize that bigger bundles = cheaper per lb Therefore you can deduce that 25lbs is the best deal per lb. Next, we ask how many 25lbs bags is between 65 and 85 lbs for the constraint. We know that 25lbs x 3 bags =75 lbs therefore $32.25 x 3 equals a total of $96.75lbs. First answer. Keep that in mind.
Second, can we get any other combination of bags that is lower than 75 lbs. The answer is YES! 1 two 25lbs bags + one 10lbs bag+ one 5lbs bag = 65 2 two 25lbs bags + two 10lbs bags =70 3 two 25lbs bags + three 5lbs bags = 65 We will also include the first combination 4 three 25lbs bags = 75
Third, We know that 2 bags of $25 is fixed (a fixed cost) in all the combinations so we can just remove that from the computations. The simplified sets are: 1 one 10lbs bag+ one 5lbs bag 2 two 10lbs bags 3 three 5lbs bags 4 one 25lbs bags
Pick any of the four and compare the others to it, To make it simple #4 has only one bag. So we have to find one that is less than $32.25. Skipping the heavy math, you can quickly reject the other combinations by doing the math in your head. 1 We know 20.43 + 13.85 is not less as ~20 + ~13= 33 > 32.25 2 We know that 20.43 *2 is not less as ~20 * 3=60 > 32.25 3 We know that 13.85 * 3 is not less as ~13 * 3=39 > 32.25
Therefore the answer is B. $96.75
Note: when I came up with the combinations, I knew that all of them had to have 2bags of 25lbs in them because 2 bags of 25lbs is cheaper than any combination of (5,10,25lbs bags)




Re: A garden center sells a certain grass seed in 5pound bags at $13.85
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