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605-655 Level|   Math Related|         
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 00:50
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The total fiber from the snack must be at least 90 grams.
Total Fiber = (Fiber from Pistachios) + (Fiber from Popcorn) + (Fiber from Almonds)
90g ≤ (200g * %Pistachio) + (150g * %Popcorn) + (100g * %Almond)

1. Lowest fiber% for Pistachio
we must assume others provide the maximun possible fiber.
max fiber from popcorn: 150g * 20% = 30g
max fiber from almonds: 100g * 10% = 10g
Total=40g

fiber of pistachio= 90g-40g => 50g
50g is 25% of 200g.

2. Lowest fiber% for Almonds
max fiber from pistachio: 200g * 27% = 54g
max fiber from popcorn: 150g * 20% = 30g
Total= 84g

fiber of almonds= 90g-84g => 6g
6g is 6% of 100g.

Hence, 25% and 6%.
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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.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 01:37
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To determine the lowest possible fiber percentage that the pistachios can have we have to first of all calculate the grams of fiber which are yielded by the other two snacks: 150 * 0.2 + 100 * 0.1 = 40 grams. Thus we know that the 200 grams of pistachios have to have at least 50 grams of fiber to meet the 90 gram goal. The proportion of fiber in the pistachios has to be at least 50 / 200 = 25%.
For the almonds we follow the same process in first determining the fiber grams which are collected consuming the two other snacks being popcorn and pistachios: 200 * 0.27 + 150 * 0.2 = 84 grams. The 100 grams of almonds have to have at least 6 grams of fiber which will be at least 6 / 100 = 6 %.

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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.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 01:45
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Let x = fiber % in pistachios
Let y= fiber % in almonds

total fiber from the snack: 200x+150(20%)+100y

Popcorn is fixed at 20% => Fiber from popcorn: 150*0.2=30
Need remaining 60g fiber from pistachios and almonds:
=> 200x+100y≥60

From the options in column can only take x = 27% (27%*200=54) and y = 6% (6%*100=6) to give the results of at least 60g fiber.

Answer: Pistachios: 27%, Almonds: 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 01:53
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In 200g pistachios have 27% = 27%*200= 54g fiber
In 150g popcorn have 20% = 20%*150= 30g fiber
In 100g almonds have 10% = 10%*100= 10g fiber

To find the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal (we call x), we have 90=x+30+10=> x =50g fiber. So the percentage will be 50/200 %= 25%

To find the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal (we call y), we have 90=54+30+y=> y =6g fiber. So the percentage will be 6/100 %= 6%
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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.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 01:58
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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.
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Lets calculate the maximum amount of fiber consumed from Arman's midday snack -
Required (R) = 90gm
Pistachie (P) = 200gm * 27% = 54gm
Popcorn (C) = 150gm * 20% = 30gm
Almonds (A) = 100gm * 10% = 10gm
Total = 54+30+10 = 94gm
Since he needs at least 90gm fiber and maximum is 94gm, this gives us a 4gm excess.

Now for the TPA. important thing to note is that both parts of this question are to be treated independently, i.e., the lowest possible fiber percentages of pistachios and almonds needn't occur together.

Part (1)
To find the lowest percentage of fiber in P, lets assume C and A are maximum.
Required fiber from P = R - C - A
P = 90 - 30 - 10 = 50gm
So, 200gm Pistachios / 50gm Fiber = 25% fiber content --- Option 5

Similarly for part (2)
To find the lowest percentage of fiber in A, lets assume P and C are maximum.
Required fiber from A = R - P - C
P = 90 - 54 - 30 = 6gm
So, 100gm Almonds / 6gm Fiber = 6% fiber content --- Option 3
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 02:18
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Given:
  • 200g pistachios (max 27% fiber)
  • 150g popcorn (max 20% fiber)
  • 100g almonds (max 10% fiber)
  • Need at least 90g total fiber


For minimum pistachios percentage:
To minimize pistachios, maximize the other two:
  • Popcorn: 150g × 20% = 30g fiber
  • Almonds: 100g × 10% = 10g fiber
  • Total from others: 30 + 10 = 40g
Pistachios must provide: 90 - 40 = 50g fiber
Minimum percentage: 50g ÷ 200g = 25%

For minimum almonds percentage:
To minimize almonds, maximize the other two:
  • Pistachios: 200g × 27% = 54g fiber
  • Popcorn: 150g × 20% = 30g fiber
  • Total from others: 54 + 30 = 84g
Almonds must provide: 90 - 84 = 6g fiber
Minimum percentage: 6g ÷ 100g = 6%

Answer:
  • Pistachios: 25%
  • Almonds: 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 02:28
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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.


I started by maximizing popcorn, since we’re not selecting its percentage --> 150*0.2= 30 gr
Now we need 90 − 30 = 60g more fiber from pistachios and almonds combined.
27% --> 200*0.27= 54 gr
10% --> 100*0.1= 10 gr

Next I checked the answer options from almonds.
The highest % for almonds is 10%, but is not among the options, so almonds must contributes less than 10g.
try with 6% = 6 gr
Then the rest of fiber (from 60g) has to come from pistachios: 60 − 6 = 54g

We already saw that 27% = 54g, so this fits perfectly.
And 27% is the highest pistachio value allowed.

ANSWER
Pistachios 27%
Almonds 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 02:32
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Correct Answer: Pistachios- 25% and Almond= 6%
Given we have,
200 grams of pistachios
150 grams of popcorn
100 grams of almonds
Maximum Fibre percentage:
pistachios 27%
Popcorn 20%
Almonds 10%
For getting minimum fibre percentage in Pistachios we need to maximise almond and popcorn, so we get
Popcorn= 150gm * 20%= 30gm
Almond= 100gm * 10%= 10gm
still 50 gm of fibre left
so now we need to include at least 25% fibre from 200gm pistachios to get 50gm fibre.

For getting minimum fibre percentage in Almond we need to maximise pistachios and popcorn, so we get
Popcorn= 150gm * 20%= 30gm
Pistachios = 200gm * 27%= 54gm
still 6 gm of fibre left
so now we need to include at least 6% fibre from 100gm almonds to get 6gm fibre.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 03:03
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For Pistachios to have the lowest possible fiber percentage, Popcorn and almonds should have the maximum possible fibre.
Popcorn= 20% = 30gms
Almonds= 10%= 10gms
So Pistachios need to have 50gms fibre, which is 25% of 200gms

For Almonds to have the lowest possible fiber percentage:
Pistachios=27%= 54gms
Popcorn = 20% = 30gms
So almonds need to have 6 gm of fibre which is 6% of 100gms
Answer: 25%, 6%
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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.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 03:08
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Given,
Mid-day snack content:
Item
Total amount
Maximum Fibre content (%)
Maximum available Fibre content (g) – by weight
Pistachios, q
200 g
27 %
54 g
Popcorn, r
150 g
20 %
30 g
Almonds, s
90 g
10 %
9 g


Nutrition goal:
“T” = 90g fibre intake
To find:
1. For Pistachios, the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal.
2. For Almonds, the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal.
Solution:
As we know,
T = q+ r + s
1. For minimum value of “q”, keeping maximum value of “r” & “s”,

90g = q + 30g + 9g

q = 51g

q% = (51/200)*100
= 25.5 %

2. For minimum value of “s”, keeping maximum value of “r” & “q”,

90g = 54 + 30g + s

s = 6g

q% = (6/90)*100
= 6.66 %

Ans :
Column 1 = 27 %
Column 2 = 20 %


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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.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 03:48
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The lowest possible fiber percentage that pistachios can have happens when popcorn and almonds have their maximum fiber percentage.
200*x/100 + 150*20/100 + 100*10/100 = 90
2x + 30 + 10 = 90
2x = 50
x = 25

The lowest possible fiber percentage that almonds can have happens when pistachios and popcorn have their maximum fiber percentage.
200*27/100 + 150*20/100 + 100*x/100 = 90
54 + 30 + x = 90
x = 6

Pistachios = 25%
Almonds = 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 03:49
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Part 1: Lowest Pistachios
to get lowest pista fiber, almond and popcorn should have maximum fibre
--> 20/100(150) + 10/100(100) = 40gm
remaining needed is 90-40 = 50gm
% of fiber in pistachios needed is 50/200 = 25%

Part 2: Lowest Almonds
to get lowest Almonds fiber, Pistachios and popcorn should have maximum fibre
--> 27/100(200) + 20/100(150) = 484gm
remaining needed is 90-84 = 6gm
% of fiber in pistachios needed is 6/100 = 6%
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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.
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p = pistachios %
q = popcorn %
a = almonds %

total fibre = 2 p + 1.5 q + a
Constraints:
1. p ≤ 27, q ≤ 20, a ≤ 10
2. total fibre ≥ 90 g

To make p as small as possible, set q and a at their max
q = 20, a = 10
-> 2 p + 1.5*20 + 10 ≥ 90
-> 2 p + 40 ≥ 90
-> p ≥ 25

To make a as small as possible, set p and q at their max
p = 27, q = 20
-> 2*27 + 1.5*20 + a ≥ 90
-> 54 + 30 + a ≥ 90
-> a ≥ 6

Answer : 25% for pistachios & 6% for almonds
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 05:19
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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 possible :
Pista : 200 * 27% = 54gm
Popcorn : 150 * 20% = 30gm
Almond : 100 *10% = 10gm

Pista has to be minimum, the 40gms from rest two. 50*100/200 = 25%
Almond to be minimum, the 84gms from rest two. 6*100/100 = 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 05:23
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We are given:

Total snack composition:

200g Pistachios

150g Popcorn

100g Almonds


Fiber content max limits:

Pistachios: up to 27%

Popcorn: up to 20%

Almonds: up to 10%


Fiber goal: at least 90g total fiber


We are to minimize fiber percentage for:

Pistachios in one case

Almonds in another
...while still meeting the 90g fiber goal, and assuming other ingredients are at maximum possible fiber content.



---

Part 1: Lowest possible fiber % for Pistachios

We assume:

Popcorn = 20% fiber → 150g × 20% = 30g fiber

Almonds = 10% fiber → 100g × 10% = 10g fiber


Total from popcorn and almonds = 30 + 10 = 40g fiber
So, pistachios must contribute at least:
→ 90 − 40 = 50g fiber

Pistachios = 200g → % fiber required = 50g / 200g = 25%

So, minimum required fiber % for pistachios = 25%


Part 2: Lowest possible fiber % for Almonds

Assume:

Popcorn = 20% fiber → 150g × 20% = 30g

Pistachios = 27% fiber → 200g × 27% = 54g


Total from popcorn + pistachios = 30 + 54 = 84g fiber
So, almonds must contribute at least:
→ 90 − 84 = 6g fiber

Almonds = 100g → % fiber required = 6g / 100g = 6%

So, minimum required fiber % for almonds = 6%



Final Answer:

Pistachios: 25%

Almonds: 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 05:30
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TO minimize fiber percentages in pistachios we have to maximize % of popcorn and almonds

200(x/100) +150(.2) + 100(.1) = 90
on solving this x will come out to be
x= 25% pistachios

TO minimize fiber percentages in Almonds we have to maximize % of popcorn and Pistachios

200(.27) + 150(x/100)+100(.1) = 90
x = 2.88~ 3% almonds
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 05:37
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27% Pistachios = 54
20% Popcorn = 30
10% almonds = 10

Goal = 90

In order to minimize a particular snack, we need to maximize other two snacks:

Min Pistachios = Goal - (Max. Almonds + Max. Popcorn) = 90 - (10 + 30) = 50
which is 25% of pistachios

Min Almonds = Goal - (Max. Pistachios + Max Popcorn) = 90 - (54 + 30) = 6
which is 6% of almonds
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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.
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Aishna1034
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 05:44
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For finding Pistachios and Almonds minimum, maximize the other as according to the percentages provided in the question. This way Pistachios is 25 and Almonds 6.
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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.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 05 Jul 2025, 05:44
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\(200\) grams of pistachios, \(150\) grams of popcorn, and \(100\) grams of almonds
The maximum fiber percentages in pistachios, popcorn, and almonds are \(27\)%, \(20\)%, and \(10\)%, respectively.
Minimum fiber requirement = 90 grams

From the details, fiber present in pistachios, popcorn and almonds is \(54 \), \(30\), & \(10\) respectively.

We are to find out the minimum possible percent of fiber the pistachios & minimum possible percent of fiber almonds can have so that Arman consumes the Minimum required fiber content of \(90\) grams.

For this we have the total maximum possible fiber content,
\(T_m = 54 + 30 + 10 = 94\)
The value can therefore reduce by \(4\) for the consumables in the \(2\) cases.

Case 1 : Pistachios have \(50\) grams of fiber; \(50 + 30 + 10 = 90\) (Rest remain constant)
This means the fiber content is \(50/200 = 25\) %

Case 2 : Almonds have \(6\) grams of fiber; \(54 + 30 + 6 = 90\)
Therefore the fiber content \(= 6/100 = 6 \) %

Therefore the correct options are:
Pistachios : \(25% \)
Almonds : \(6%\)
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