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A garden center sells a certain grass seed in 5-pound bags at $13.85 SORT BY: Tags: Show Tags Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 94614 Own Kudos [?]: 643727 [218] Given Kudos: 86749 Most Helpful Reply Retired Moderator Joined: 08 Dec 2013 Status:Greatness begins beyond your comfort zone Posts: 2091 Own Kudos [?]: 8993 [39] Given Kudos: 171 Location: India Concentration: General Management, Strategy GPA: 3.2 WE:Information Technology (Consulting) Tutor Joined: 16 Oct 2010 Posts: 15150 Own Kudos [?]: 66865 [24] Given Kudos: 436 Location: Pune, India RC & DI Moderator Joined: 02 Aug 2009 Status:Math and DI Expert Posts: 11482 Own Kudos [?]: 34591 [13] Given Kudos: 325 Re: A garden center sells a certain grass seed in 5-pound bags at$13.85 [#permalink]
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niks18 chetan2u gmatbusters pushpitkc pikolo2510

Quote:
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 $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 Skywalker18 Quote: 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 General Discussion Manager Joined: 02 Mar 2012 Posts: 198 Own Kudos [?]: 299 [7] Given Kudos: 4 Schools: Schulich '16 Re: A garden center sells a certain grass seed in 5-pound bags at$13.85 [#permalink]
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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 65-80.if there are more cases it will obviously be more than $100 IIM School Moderator Joined: 04 Sep 2016 Posts: 1249 Own Kudos [?]: 1265 [0] Given Kudos: 1207 Location: India WE:Engineering (Other) A garden center sells a certain grass seed in 5-pound bags at$13.85 [#permalink]
niks18 chetan2u gmatbusters pushpitkc pikolo2510

Quote:
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 $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 Skywalker18 Quote: 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. GMAT Club Legend Joined: 19 Dec 2014 Status:GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Posts: 21835 Own Kudos [?]: 11799 [6] Given Kudos: 450 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A garden center sells a certain grass seed in 5-pound bags at$13.85 [#permalink]
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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: GMAT assassins aren't born, they're made, Rich Target Test Prep Representative Joined: 14 Oct 2015 Status:Founder & CEO Affiliations: Target Test Prep Posts: 19199 Own Kudos [?]: 22718 [6] Given Kudos: 286 Location: United States (CA) Re: A garden center sells a certain grass seed in 5-pound bags at$13.85 [#permalink]
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Bunuel wrote:
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 $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.

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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink] 2 Kudos Expert Reply Bunuel wrote: 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$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 $$= \frac{13.85}{5} =$$ almost$3 per pound.
10-pound bags $$= \frac{20.43}{10} =$$ a bit more than $2 per pound. 25-pound bags $$= \frac{32.25}{25} =$$ 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. Director Joined: 04 Jun 2020 Posts: 542 Own Kudos [?]: 74 [1] Given Kudos: 623 A garden center sells a certain grass seed in 5-pound bags at$13.85 [#permalink]
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Bunuel wrote:
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 $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

Bunuel

I fell for the trap and thought that getting exactly 65 pounds would be the most cost effective (starting with using 2 bags of 25 pounds, then 1 10-pound bag, and 1 5-pound bag). If you were approaching this from a fresh start, would you have first maximized the number of the 25 bags (so 3 bags) and then compared it to the original calculation I did of trying to find 65 pounds?

I am just trying to think of how someone would have laid this out strategically without wasting too much time fidgeting with the numbers.

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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink] 1 Kudos Expert Reply woohoo921 wrote: Bunuel wrote: 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$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 Bunuel I fell for the trap and thought that getting exactly 65 pounds would be the most cost effective (starting with using 2 bags of 25 pounds, then 1 10-pound bag, and 1 5-pound bag). If you were approaching this from a fresh start, would you have first maximized the number of the 25 bags (so 3 bags) and then compared it to the original calculation I did of trying to find 65 pounds? I am just trying to think of how someone would have laid this out strategically without wasting too much time fidgeting with the numbers. Thanks for your help! Even before reading your post, I read the question first and when I got to this part: a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, I thought to myself, OK I'd probably have to calculate price for 65 pounds and for 3*25 pounds to see which one will cost less, otherwise what that part is doing there in the stem ? GMAT Club Legend Joined: 19 Dec 2014 Status:GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Posts: 21835 Own Kudos [?]: 11799 [1] Given Kudos: 450 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A garden center sells a certain grass seed in 5-pound bags at$13.85 [#permalink]
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woohoo921 wrote:
Bunuel wrote:
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 $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

Bunuel

I fell for the trap and thought that getting exactly 65 pounds would be the most cost effective (starting with using 2 bags of 25 pounds, then 1 10-pound bag, and 1 5-pound bag). If you were approaching this from a fresh start, would you have first maximized the number of the 25 bags (so 3 bags) and then compared it to the original calculation I did of trying to find 65 pounds?

I am just trying to think of how someone would have laid this out strategically without wasting too much time fidgeting with the numbers.

Hi woohoo921,

It's important to remember that nothing about a GMAT question is ever 'random' - all of the words and numbers are carefully chosen, so it's often beneficial to think in terms of "why" (re: WHY was I told this specific piece of information?). 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.

Many Test Takers would focus on buying exactly 65 pounds of seed, but 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 is the actual lowest price possible.

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

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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85 [#permalink] hi Bunuel , avigutman, I was confused by this Q at first I thought it was asking which following options is least chance for this purchase to happen, while when I checked the answer , it is asking the min amount of the purchase IMO, possible refers to lease chance of something to happen, likely refers to how high/low something happen would you help clarify ? thanks in advance Re: A garden center sells a certain grass seed in 5-pound bags at$13.85 [#permalink]
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