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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake

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mvgkannan

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04 Jul 2025, 11:53

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$x = 20%, y= 15%, z= 10%$ The maximum percentage of fiber.
Also
$Total Fiber = 200x + 150y + 100z$.

Minimum Fiber = 90.

So for minimum pistachio fiber %,

$\\
90 = 200x + 150*0.20 + 100*0.10\\
x=25%\\
$
So for minimum almond fiber %,

$\\
90 = 200*0.27 + 150*0.20 + 100*z\\
z=6%\\
$

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Bunuel

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Lowest possible of fiber from Pistachios will happen when the fiber content from other source is maximum.

Max possible % of fiber from popcorn = 20%
Max possible value of fiber from 150 grams of popcorn = 20% of 150 = 30 grams

Max possible % of fiber from almonds= 10%
Max possible value of fiber from 100 grams of popcorn = 10% of 100 = 10 grams

Deficient = 90 - (30 + 10) = 50

This 50 grams should come from Pistachios

% = 50/200 * 100= 1/4 *100= 25%

Lowest possible of fiber from Almonds will happen when the fiber content from other sources is maximum.

Max possible % of fiber from popcorn = 20%
Max possible value of fiber from 150 grams of popcorn = 20% of 150 = 30 grams

Max possible % of fiber from Pistachios = 27%
Max possible value of fiber from 200 grams of popcorn = 27% of 200 = 54 grams

Deficient = 90 - (30 + 54) = 6

This 6 grams should come from Almonds

% = 60/100 *100 = 6%

Almonds = 6%
Pistachios = 25%

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04 Jul 2025, 12:31

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Fibre >= 90 gm

Pistachio = 200 = 27% fiber = 54
Popcorn = 1500 = 20% fiber = 30
Almond = 100 = 10% fiber = 10

to minimize pistachio, maximize popcorn, and almond, then total from both. = 30+10 = 40, rest 50 will come from Pistachio
then = 50/200 = 25%

to minimize Almond, maximize popcorn, and Pistachio, then total from both. = 54+30 = 84, rest 6 will come from Almond
then = 6/100 = 6%

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04 Jul 2025, 13:09

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Option E and Option C are the correct answers.

First lets understand what the question is telling us and what we need to find in order to answer the question.

The question starts with telling us Arman is tracking his fiber intake. Then it tells us the items and the quantity of the items which he has consumed on that day and what was his target for fiber consumption from those items. Then it goes on to tell the maximum percent of fiber which those items could contain. And then asking us to find the finding fiber percentage of 2 items i.e. 'Pistachios' and 'Almonds' which fill result in 90 gram of fiber consumption.

So now after understand the information mentioned in the question and what we need to find in order to answer the question lets solve the question.

As the question tells us that Arman consumed "200 grams of pistachios, 150 grams of popcorn, and 100 grams of almonds" which contains "maximum fiber percentages in pistachios, popcorn, and almonds are 27%, 20%, and 10%, respectively". Lets also assume pistachios to be 'x', popcorn to be 'y' and almonds to be 'z'.

So lets calculate how much maximum fiver each one of them will contain:

Pistachios (x): 200 grams were consumed by Arman and it contain a maximum of 27% fiber
x ≤ 200*27%
x ≤ 200*(0.27)
x ≤ 54

Popcorn (y): 150 grams were consumed by Arman and it contain a maximum of 20% fiber
y ≤ 150*20%
y ≤ 150*(0.20)
y ≤ 30

Almonds (z): 100 grams were consumed by Arman and it contain a maximum of 10% fiber
z ≤ 100*10%
z ≤ 100*(0.10)
z ≤ 10

Now the question asks us "[color=#0f0f0f]lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal" and "lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal".[/color]

We all know the best possible way to find the lowest possible percentage is by maximizing the percentage of other two food items so that the last food item can contribute the lowest.

So, as we know from the question 'x + y + z = 90'

In order to find the "[color=#0f0f0f]lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal" we will take the maximum value for Popcorn and Almond which will be 30 and 10 respectively.[/color]

So, x + 30 + 10 = 90
x +40 = 90
x = 50

Here lets take the fiber percentage of Pistachios to be 'P'.

x = 200*(P%)
50 = 200*(P%)
(50/200) = P%
0.25 = P% here we can notice that the value of 'P' is in numbers but we want it to be in percentage so for that we need to multiply the number with '100'.
0.25*100 = P%
25% = P% (Option E)

Now lets find the "[color=#0f0f0f]lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal" we will take the maximum value for Popcorn and Pistachios which will be 30 and 54 respectively.
54 + 30 + z = 90[/color]
84 + z = 90
z = 6

Here lets take the fiber percentage of Almonds to be 'A'.

z = 100*(A%)
6 = 100*(A%)
0.06 = A% here also as it is in numeric for and to convert it into percentage we will multiply it by '100'.
0.06*100 = A%
6% = A% (Option C)

Bunuel

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04 Jul 2025, 14:05

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Solution:

We are given in the question stem that Midday snacks consist of 200 grams of pistachios, 150 grams of popcorn, and 100 grams of almonds. And, the maximum fiber percentages in pistachios, popcorn, and almonds are 27%, 20%, and 10%. To maintain the 90-gram fiber goal from the snack, we can calculate the maximum percentage given in the question stem.

1. Pistachios -200*$\frac{27}{100}$=54
2. Popcorn - 150*$\frac{20}{100}$= 37
3. Almonds- 100*$\frac{10}{100}$=10

And the total of all comes down to 94. So, it covers our minimum requirement 90-gram fiber goal.

Same way, we have to search among the options, which choice meets the minimum requirement of a 90-gram fiber goal from the lowest possible fiber percentage that pistachios can have and the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal. The only choice that fits our answer choice is 27% of Pistachios and 25% of almonds. Here we can see the same:

Pistachios- 200*$\frac{27}{100}$=54
Almonds - 150*$\frac{25}{100}$=37.7

And the total of both is 91. So, 27% for Pistachios and 25% for Almonds.

Bunuel

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04 Jul 2025, 14:25

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For Pistachio to have lowest fiber, remaining two (Almonds and popcorn) should have highest fiber.
So Maximum fiber in popcorn = 150*0.2 =30
maximum fiber in Almonds = 100*0.1 =10

So lowest possible fiber for pistachios = 90 - (30+10) =50 . i.e 25% of 200
So Lowest fiber percent for Pistachios= 25%

similarly for almonds,

Maximum fiber in Pistachios = 200*0.27 = 54
maximum fiber in popcorn = 150*0.2 =30.

So lowest possible fiber for almonds = 90 - (30+54)=6 i.e 6% of 100
So Lowest fiber percent for almonds = 6%

Bunuel

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04 Jul 2025, 15:03

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First, we calculate the Maximum amount of fiber in each of the nuts.

	pistachios	popcorn	almonds
Total weight	200	150	100
Max Fiber percentage	27%	20%	10%
Max Fiber weight	54	30	10

So, the maximum amount of fiber he can get from the snack is 54+30+10=94.
He only needs 90 grams to meet his goal, so there are 4 grams of extra fiber that we can work with to answer the question.

If we deduct all of the 4 grams from the pistachios' fiber content, then it will have 54-4=50 grams of fiber in 200 grams.

So the percentage of fiber content is $\frac{50}{200}*100 =25%$

If we deduct all of the 4 grams from the almond's fiber content, then it will have 10-4=6 grams of fiber in 100 grams.

So the percentage of fiber content is $\frac{6}{100} *100 =6%$

Bunuel

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Question analysis: If we are to find the lowest percentages for Pistachios and Almonds, the we must consider the greatest percentage for other substances.

Treating question data:
- Needed amount of fiber: 90g
- Intake of substances, maximum percentage and weight of fiber:
Pistachio: 200g | 27% -> 54g
Popcorn: 150g | 20% -> 30g
Almonds: 100g | 10% -> 10g

Finding Pistachio least percentage:
*we must consider Popcorn and Almond greatest percentages, which give us a fiber intake of 10g + 30g = 40g.
Therefore, there is a lack of 50g of fiber to be supplied with 200g of pistachio, resulting in a lowest percentage of 25%

Finding Almond least percentage:
*we must consider Popcorn and Pistachio greatest percentages, which give us a fiber intake of 54g + 30g = 84g.
Therefore, there is a lack of 6g of fiber to be supplied with 100g of almonds, resulting in a lowest percentage of 6%
----------------------
Arman is tracking his fiber intake for the day. His midday snack consists of 200 grams of pistachios, 150 grams of popcorn, and 100 grams of almonds. To meet his nutritional goal, he must consume at least 90 grams of fiber from the snack. The maximum fiber percentages in pistachios, popcorn, and almonds are 27%, 20%, and 10%, respectively.

Select for Pistachios the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal, and select for Almonds the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal. Make only two selections, one in each column.

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04 Jul 2025, 18:16

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Arman is tracking his fiber intake for the day. His midday snack consists of 200 grams of pistachios, 150 grams of popcorn, and 100 grams of almonds. To meet his nutritional goal, he must consume at least 90 grams of fiber from the snack. The maximum fiber percentages in pistachios, popcorn, and almonds are 27%, 20%, and 10%, respectively.

Max Fiber intake can be: P = .27 * 200 = 54; Pop = .2 * 150 = 30; A = .1 * 100 = 10;

Select for Pistachios the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal, and select for Almonds the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal. Make only two selections, one in each column.

For Pistachios to contain minimum fiber, the other two should have maximum fiber -> 30 + 10 = 40; Remaining 90 - 40 = 50 needed from 200 gram pistachios; so %age = (50/200)*100 = 25%

For Almonds to contain minimum fiber, the other two should have maximum fiber -> 54 + 30 = 84; Remaining 90 - 84 = 6 needed from 100 gram almonds; so %age = (6/100)*100 = 6%

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04 Jul 2025, 19:22

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Assume the fiber percentages are maxed, total fiber = 200 x 27% + 150 x 20% + 100 x 10% = 54 + 30 + 10 = 94, leaving 4g fiber over 90g.

If almonds % is maxed, Pistachios % can be 50/200 = 25%
If pistachios % is maxed, almonds % can be 6/100 = 6%

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04 Jul 2025, 19:42

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Max possible fibre quantities:
Pistachios = 200 * 0.27 = 54
Popcorn = 150 * 0.20 = 30
Almonds = 100 * 0.10 = 10

%PImin = (90 - 30 - 10) / 200 = 0,25
%ALmin = (90 - 54 - 30) / 100 = 0,06

Bunuel

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04 Jul 2025, 20:27

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Pistachio - 200 gms, max fibre: 27% - max fibre - 54 gms
Popcorn - 150 gms, fibre 20% (the question only asks for pistachio and almonds so popcorn's fibre qty needs to be assumed the maximum in order to figure out the two cases) - 30 gms
Almonds - 100 gms, max fibre - 10% - max fibre - 10 gms

Now, we are told that 90 gms of fibre needs to be maintained.
If we keep almonds and popcorn maximum, we will get 40 gms of fibre. Remaining 50 gms needs to be sourced from pistachio. 50/200 *100 = 25%
So minimum % of pistachio possible is 25%

Let's say with pistachio we achieve the maximum - 54 gms fibre.
Popcorn gives us 30 gms.
So in total we have 84 gms of fibre. remaining 6 needs to come from almonds.
therefore 6/100 = 6% from almonds is the bare minimum.

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04 Jul 2025, 21:45

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Arman is tracking his fiber intake for the day. His midday snack consists of 200 grams of pistachios, 150 grams of popcorn, and 100 grams of almonds. To meet his nutritional goal, he must consume at least 90 grams of fiber from the snack. The maximum fiber percentages in pistachios, popcorn, and almonds are 27%, 20%, and 10%, respectively.

Select for Pistachios the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal, and select for Almonds the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal. Make only two selections, one in each column.

Fiber in Pistachios= 200gm * 27/100= 54 gm
Fiber in popcorn = 150*20/100=30 gm
Fiber in almonds= 100*10/100= 10 gm

Total fiber= 54+30+10=94 gm

Lowest possible % fiber in pistachios= 90-40= 50 gm = 200*x/100, Thus x= 25 %

Lowest possible % fiber in almonds = 90-54-30= 6 gmm= 100*y/100, y= 6%

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Bunuel

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Answer: Pistachios – 25%, Almonds – 6%

I. So we need 90g fiber total. If I try to keep pistachios at the lowest possible %, I’ll max out popcorn and almonds. Popcorn gives 150g × 20% = 30g, almonds give 100g × 10% = 10g. That’s 40g. So pistachios need to give 50g. 50g out of 200g = 25%. That works.

II. Now if I want almonds at the lowest %, I’ll max out popcorn (30g) and pistachios (200g × 27% = 54g), that gives 84g. Almonds just need to give 6g → 6g out of 100g = 6%. That’s the lowest possible for almonds that still hits the goal.

Thus 25% for pistachios and 6% for almonds

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04 Jul 2025, 21:51

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Bunuel

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Maximum Fiber in pistachios = 200 * 27% = 54
Maximum Fiber in popcorn = 150 * 20% = 30
Maximum Fiber in almonds = 100 * 10% = 10

1. Pistachios
Now if we have to find the lowest percentage in pistachios, we have to keep the other components maximum
=> P+ Pop + A = 90
=> P + 30 + 10 = 90
=> P = 50

So to get 50 grams of protein from 200 grams we need $\frac{50}{200} * 100$ = 25%

1. Almonds
Now if we have to find the lowest percentage in almonds, we have to keep the other components maximum
=> P+ Pop + A = 90
=> 54 + 30 + A = 90
=> A = 6

So to get 6 grams of protein from 100 grams we need $\frac{6}{100} * 100$ = 6%

Pistachios = 25%
Almonds = 6%

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04 Jul 2025, 21:54

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200g Pistachios contain maximum 27% fiber
150g Popcorn contain maximum 20% fiber
100g Almonds contain maximum 10% fiber

200g pistachios = 54g fiber max
150g popcorn = 30g fiber max
100g almonds = 10g fiber max

at least 90g fiber to be eaten

for lowest possible fiber percentage in 200g pistachios assume max fiber is getting to the body from popcorn and almonds

10g almonds fiber + 30g popcorn fiber = 40g of fiber

90g-40g = 50g more needed, which will be met by pistachios

50g/200g = 25%

similarily, we will do for almonds

6/100 = 6%

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04 Jul 2025, 22:43

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	Weight, g	Fiber %	Fiber, g
Pistachios	200	27	54
Popcorn	150	20	30
Almonds	100	10	10
Total			94

The fiber intake is 4g more than requirement. This 4g fiber can be reduced in any of one the snacks or different snack types combined. To get lowest possible fiber weight can be achieved by reducing 4g in only one type of snack

Pistachios: Lowest possible fiber requirement $=50g$

Fiber percent in pistachios $= \frac{50}{200}*100=25\text{%}$

Almonds: Lowest possible fiber requirement $=6g$
Fiber percent in Almonds$= \frac{6}{100}*100=6 \text {%}$

Pistachios: 25%
Almonds: 6%

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The max value of fiber would be 54, 30 and 10 gm from pistachio popcorn and almonds. Now to minimise 1 we would maximise other 2. For pistachios we would need atleast 50 so other 2 would be 40 and would meet the goal. So 25% and for almond it would be 90-84=6 so 6%

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04 Jul 2025, 23:50

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Find lowest possible % fiber for:

Pistachios, assuming popcorn and almonds at max

Almonds, assuming popcorn and pistachios at max

Find lowest % for Pistachios
Assume:
Popcorn = 150g × 20% = 30g
Almonds = 100g × 10% = 10g
Total from others = 30 + 10 = 40g
So, pistachios must provide = 90 − 40 = 50g

Now:
200g pistachios must provide 50g
==>Percentage calculation= 50 / 200 = 25%
Lowest pistachio % = 25%

2)Find lowest % for Almonds

Assume:
Popcorn = 150g × 20% = 30g
Pistachios = 200g × 27% = 54g
Total = 30 + 54 = 84g
Almonds must provide = 90 − 84 = 6g

Now:
100g almonds must provide 6g
==>Percentage calculation = 6 / 100 = 6%

Lowest almond % = 6%

LunaticMaestro

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04 Jul 2025, 23:57

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(1) to find fibre content in pistachios.

> 20% fibre from popcorn (150g) = 30gm fibre
> 10% fibre from almonds (100g) = 10gm
remain = 90 - (30 +10) = 50gm

50gm fibre from 200 gm pistachios = 25%

(2) to find fibre % in almonds
> 27% fib from 200gm pistachios = 54gm
> 20% fib from 150gm popcorn = 30 gms

remain = 90 - (54+30) = 6 gms
6gm from 100gms almonds = 6%