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

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

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

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I was not able to understand below quote by Skywalker18


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.

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

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

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.

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 ?

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

Contact Rich at: Rich.C@empowergmat.com

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