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A trail mix company keeps costs down by employing the Updated on: 12 Dec 2024, 03:27
Originally posted by Nanobotstv on 01 Oct 2016, 12:59.
Last edited by Bunuel on 12 Dec 2024, 03:27, edited 2 times in total.
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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) 40%
(B) 48%
(C) 49%
(D) 50%
(E) 60%
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B
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A trail mix company keeps costs down by employing the 01 Oct 2016, 20:14
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alanforde800Maximus
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%

Please assist with above problem.
Show more

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= \(\frac{4}{10}*100\)%..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 % =\(\frac{(50-26)}{50}=\frac{24}{50}=48\)%

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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A trail mix company keeps costs down by employing the 04 Sep 2017, 06:03
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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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The actual answer is 48%.

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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A trail mix company keeps costs down by employing the 01 Oct 2016, 22:31
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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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A trail mix company keeps costs down by employing the 02 Oct 2016, 02:40
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deepthit
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 ??
Show more

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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A trail mix company keeps costs down by employing the 02 Oct 2016, 03:27
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deepthit
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..
Show more

Thank you for the clarification. I interpreted the question wrongly.
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A trail mix company keeps costs down by employing the 18 Oct 2016, 20:17
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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
alanforde800Maximus
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%

Please assist with above problem.

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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A trail mix company keeps costs down by employing the 03 Sep 2017, 05:38
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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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A trail mix company keeps costs down by employing the 11 Apr 2018, 20:56
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Currently peanuts are 50 and other are 25. So peanuts can be reduced to max 26 in number.

26/50 corresponds to 52percent.
Means it can reduce by 48 percent

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Nanobotstv
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) 40%
(B) 48%
(C) 49%
(D) 50%
(E) 60%

Please assist with above problem.
Show more


The peanuts: cashews: almonds ratio is 10:4:1
Peanuts ratio= 10/10+4+1= 10/15=2/3
Cashews ratio= 4/15
Almonds ratio= 1/15

Total nuts=75
Actual peanuts in the bag= 2/3*75=50
Actual cashews in the bag= 4/15*75=20
Actual almonds in bag= 1/15*75=5

----Decrease peanuts such that it still constitutes 50%----
50% of 50= 25

The least peanuts that should be there is 26
x% of 50= change in the number of peanuts
x% * 50= 24
x=48%

option B
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A trail mix company keeps costs down by employing the 23 Nov 2022, 20:08
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Given: 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.

Asked: 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?

Number of peanuts in bag of 75 nuts = 10/15*75 = 50
Minimum number of peanuts required = 26

The maximum percentage by which the company could decrease its number of peanuts per bag = (50 - 26)/50 *100% = 48%

(A) 40%
(B) 48%
(C) 49%
(D) 50%
(E) 60%

IMO B
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A trail mix company keeps costs down by employing the 04 Dec 2022, 01:49
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KarishmaB

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%
Show more

Hi KarishmaB,

I have a doubt here.

When we are decreasing the quantity of peanuts, why are we not keeping the original ratio of 10:4:1 for the nuts?
The number of peanuts should be more than half of the total nuts = 75/2 = 37.5

I interpreted this as
P. : C. : A
50 : 20 : 5
A decrease of 5 peanuts will lead to an increase of 4 Cashew and 1 almond.
45 : 24 : 6
40: 28 : 7

So, maximum reduction possible is 40 peanuts as nuts can’t be in decimals.
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A trail mix company keeps costs down by employing the 04 Dec 2022, 05:48
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Noida
KarishmaB

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%

Hi KarishmaB,

I have a doubt here.

When we are decreasing the quantity of peanuts, why are we not keeping the original ratio of 10:4:1 for the nuts?
The number of peanuts should be more than half of the total nuts = 75/2 = 37.5

I interpreted this as
P. : C. : A
50 : 20 : 5
A decrease of 5 peanuts will lead to an increase of 4 Cashew and 1 almond.
45 : 24 : 6
40: 28 : 7

So, maximum reduction possible is 40 peanuts as nuts can’t be in decimals.
Show more

Currently the peanuts are 2/3rd i.e. 66.66%. We are asked to reduce the peanuts so that they constitute at least 50% of the total mix. We are only asked to reduce the number of peanuts per bag, not increase the number of cashews and almonds to make up for the reduction.
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A trail mix company keeps costs down by employing the 09 Apr 2025, 02:37
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more than half of total amount of nut , should be more than 37.5 ,no?
Nanobotstv
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) 40%
(B) 48%
(C) 49%
(D) 50%
(E) 60%
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A trail mix company keeps costs down by employing the 09 Apr 2025, 05:54
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shubhim20
more than half of total amount of nut , should be more than 37.5 ,no?
Nanobotstv
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) 40%
(B) 48%
(C) 49%
(D) 50%
(E) 60%
Show more
Please refer the first post: https://gmatclub.com/forum/a-trail-mix- ... l#p1742436

Nuts are upto 75 per bag.
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