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# A trail mix company keeps costs down by employing the peanuts:cashews:

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Manager
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A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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01 Oct 2016, 12:59
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Question Stats:

21% (02:01) correct 79% (01:58) wrong based on 103 sessions

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A trail mix company keeps costs down by employing the peanuts:cashews:almonds ratio of 10:4:1 in each bag of up to 75 total nuts. What is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts?

(A) 30%
(B) 40%
(C) 49%
(D) 50%
(E) 60%

[Reveal] Spoiler: OA

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Re: A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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01 Oct 2016, 20:14
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Expert's post
alanforde800Maximus wrote:
A trail mix company keeps costs down by employing the peanuts:cashews:almonds ratio of 10:4:1 in each bag of up to 75 total nuts. What is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts?

(A) 30%
(B) 40%
(C) 49%
(D) 50%
(E) 60%

Hi,
We are not aware the exact numbers it could be minimum 10+4+1 or 75..
If it is 15, there are 10 peanuts and remaining 5 of others..
To be still more than 50%, peanuts should be more than 5, say least 6..
So from 10, we can get it down to 6.
So % decrease is 4 out of 10= 4/10*100%..40%

But say bag was full...75
So peanuts were 50 and others 75-50=25...
Peanuts can be 26 and still be more than 50%..
So decrease % =(50-26)/50=24/50=48%

Here we are not aware how many nuts are there in total, so 40% or less decrease will ensure that peanuts are>50%

B
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Manager
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Re: A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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01 Oct 2016, 22:31
chetan2u,

I tried to do something like this

75 is the total and when divided as per ratio, they would be 50 : 20 : 5

Since the reduction would be evenly distributed trough out for all the nuts, i took LCM for 10, 4, 1 and LCM is 20 .

So decided that the percentage discounted would be multiple of 20 i.e from options the possible values are 20, 40

when i applied rule that peanuts should be half for 20 % decrease, the ratio will be 30 : 12: 3 - which satisfies the condition

now taking 40% decrease, the ratio will be 20 : 8: 2 which constitute exactly half - which does not satisfy the condition that peanuts should be more than half.

So it should be 20 %

Is this approach right ??

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Re: A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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02 Oct 2016, 02:40
2
KUDOS
Expert's post
deepthit wrote:
chetan2u,

I tried to do something like this

75 is the total and when divided as per ratio, they would be 50 : 20 : 5

Since the reduction would be evenly distributed trough out for all the nuts, i took LCM for 10, 4, 1 and LCM is 20 .

So decided that the percentage discounted would be multiple of 20 i.e from options the possible values are 20, 40

when i applied rule that peanuts should be half for 20 % decrease, the ratio will be 30 : 12: 3 - which satisfies the condition

now taking 40% decrease, the ratio will be 20 : 8: 2 which constitute exactly half - which does not satisfy the condition that peanuts should be more than half.

So it should be 20 %

Is this approach right ??

Hi,

There is a bit of misunderstanding of the Q in above method..
The decrease is ONLY of peanuts..
Thus the ratio that has to be decreased is 50 in 50:20:5....
So remove some out of 50 such that the SUM of other two 20+5 becomes less than half..
_________________

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Re: A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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02 Oct 2016, 03:27
1
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chetan2u wrote:
deepthit wrote:
chetan2u,

I tried to do something like this

75 is the total and when divided as per ratio, they would be 50 : 20 : 5

Since the reduction would be evenly distributed trough out for all the nuts, i took LCM for 10, 4, 1 and LCM is 20 .

So decided that the percentage discounted would be multiple of 20 i.e from options the possible values are 20, 40

when i applied rule that peanuts should be half for 20 % decrease, the ratio will be 30 : 12: 3 - which satisfies the condition

now taking 40% decrease, the ratio will be 20 : 8: 2 which constitute exactly half - which does not satisfy the condition that peanuts should be more than half.

So it should be 20 %

Is this approach right ??

Hi,

There is a bit of misunderstanding of the Q in above method..
The decrease is ONLY of peanuts..
Thus the ratio that has to be decreased is 50 in 50:20:5....
So remove some out of 50 such that the SUM of other two 20+5 becomes less than half..

Thank you for the clarification. I interpreted the question wrongly.

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Re: A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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18 Oct 2016, 20:17
Hi - I understand the 48% figure, but why do you chose 40% then? Is it because it's the highest choice less than the figure you arrived at (48%)?

chetan2u wrote:
alanforde800Maximus wrote:
A trail mix company keeps costs down by employing the peanuts:cashews:almonds ratio of 10:4:1 in each bag of up to 75 total nuts. What is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts?

(A) 30%
(B) 40%
(C) 49%
(D) 50%
(E) 60%

Hi,
We are not aware the exact numbers it could be minimum 10+4+1 or 75..
If it is 15, there are 10 peanuts and remaining 5 of others..
To be still more than 50%, peanuts should be more than 5, say least 6..
So from 10, we can get it down to 6.
So % decrease is 4 out of 10= 4/10*100%..40%

But say bag was full...75
So peanuts were 50 and others 75-50=25...
Peanuts can be 26 and still be more than 50%..
So decrease % =(50-26)/50=24/50=48%

Here we are not aware how many nuts are there in total, so 40% or less decrease will ensure that peanuts are>50%

B

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Re: A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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03 Sep 2017, 05:38
Why wouldn't it be 45% (answer that is not included)?

We know the ratio to be 10x:4x:x. x <= 5, given that the total number of peanuts must be less than 75.

Let y be the number of peanuts to be subtracted:
(10x-y)/(15x-y) > 0.5
2.5x > 0.5y
5x > y

Therefore, y must be less than 5x.
At first glance, it appears that y must decrease in increments of x (i.e., 4x, 3x, 2x, x), but isn't that not true?
If x = 2, and y = 4.5x, the new ratio of peanuts is 11/21 = 0.52, which is greater than 50%.

Can anyone help?
VeritasPrepKarishma Bunuel

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Re: A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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04 Sep 2017, 06:03
tlaw wrote:
Why wouldn't it be 45% (answer that is not included)?

We know the ratio to be 10x:4x:x. x <= 5, given that the total number of peanuts must be less than 75.

Let y be the number of peanuts to be subtracted:
(10x-y)/(15x-y) > 0.5
2.5x > 0.5y
5x > y

Therefore, y must be less than 5x.
At first glance, it appears that y must decrease in increments of x (i.e., 4x, 3x, 2x, x), but isn't that not true?
If x = 2, and y = 4.5x, the new ratio of peanuts is 11/21 = 0.52, which is greater than 50%.

Can anyone help?
VeritasPrepKarishma Bunuel

Say bag had total 75 nuts - the maximum possible
So peanuts were 50 and others 75-50=25
Peanuts can be 26 and still be more than 50%
So decrease % =(50-26)/50=24/50=48%
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Re: A trail mix company keeps costs down by employing the peanuts:cashews: [#permalink]

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04 Sep 2017, 06:06
VeritasPrepKarishma - Thank you!
Then is the answer key to this question incorrect?

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Re: A trail mix company keeps costs down by employing the peanuts:cashews:   [#permalink] 04 Sep 2017, 06:06
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