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

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

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New post 03 Jul 2016, 11:17
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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

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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85  [#permalink]

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New post 29 Jun 2018, 21:12
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adkikani wrote:
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
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85  [#permalink]

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New post 03 Jul 2016, 11:31
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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 5-pound bags at $13.85  [#permalink]

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New post 04 Jul 2016, 00:09
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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
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85  [#permalink]

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

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New post 08 Apr 2018, 12:47
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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 5-pound bags at $13.85  [#permalink]

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New post 08 Apr 2018, 13:47
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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 5-pound bags at $13.85  [#permalink]

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New post 19 May 2018, 15:49
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


This is a straight forward question with a straight-forward method to solve. However, a lot of time gets eaten up while solving and eliminating wrong answers. What time-efficient 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 5-pound bags at $13.85  [#permalink]

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New post 29 Jun 2018, 21:00
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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.
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85  [#permalink]

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New post 02 Oct 2018, 21:22
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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.

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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85  [#permalink]

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New post 03 Oct 2018, 17:56
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.

Answer: B
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85  [#permalink]

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New post 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 5-pound bags at $13.85  [#permalink]

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New post 07 Nov 2018, 00:11
chetan2u wrote:
adkikani wrote:
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


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 5-pound bags at $13.85  [#permalink]

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New post 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)
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A garden center sells a certain grass seed in 5-pound bags at $13.85  [#permalink]

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New post Updated on: 12 Jul 2019, 06:08
This is a poorly worded question - shame on GMAC. It does not ask for "minimum possible cost per pound".

Originally posted by mykrasovski on 05 Jul 2019, 08:57.
Last edited by mykrasovski on 12 Jul 2019, 06:08, edited 1 time in total.
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85  [#permalink]

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New post 12 Jul 2019, 01:33
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


Responding to a pm:

5 pound bag - $13.85
10 pound bag - $20.43 (the cost would be about $27 with two 5 pound bags so the 10 pound bag is much cheaper in terms of $/kg)
25 pound bag - $32.25 ($32 is much less than $40, the cost of two 10 pound bags so a 25 pound bag is much cheaper in terms of $/kg)

65 <= Quantity to Buy <= 80
It is best to buy as many 25 pound bags as possible to make up the quantity. So let's buy 2 25 pounds bags to make up 50 pounds. Now we are left with 15 tp 30 pounds to fill. We can do this is following ways:
1. Buy another 25 pound bag for $32.25
2. Buy two 10 pound bags for $40.86 (Ignore since it is more expensive than case 1)
3. Buy one 10 pound and one 5 pound bag for about $34 (Ignore since it is more expensive than case 1)

Hence, we should simply buy three 25 pound bags for $32.25*3 = $96.75

Answer (B)
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Re: A garden center sells a certain grass seed in 5-pound bags at $13.85   [#permalink] 12 Jul 2019, 01:33
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