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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 08:00
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Pistachios: 25% 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.
Pistachios Almonds
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6%
20%
25%
27%
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Pistachios: 25% Almonds: 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 08:30
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Bunuel
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 Official Explanation:



We are given that 200 * P + 150 * C + 100 * A must be greater than or equal to 90, where P, C and A, are fiber percentages in pistachios, popcorn, and almonds, respectively.

200 * P + 150 * C + 100 * A ≥ 90

The maximum fiber percentages are:

Maximum fiber percentage in pistachios = 27%
Maximum fiber percentage popcorn = 20%
Maximum fiber percentage almonds = 10%

General rule for such problems:

To maximize one quantity, minimize the others.
To minimize one quantity, maximize the others.


Minimizing P:

To find the minimum value of P for which 200 * P + 150 * C + 100 * A ≥ 90 holds, we maximize C and A. Using C = 0.20 and A = 0.10, we get:

200 * P + 150 * 0.20 + 100 * 0.10 ≥ 90
200 * P + 30 + 10 ≥ 90
P ≥ 50/200 = 0.25

Thus, the minimum value of P is 25%.

Minimizing A:

To find the minimum value of A for which 200 * P + 150 * C + 100 * A ≥ 90 holds, we maximize P and C. Using P = 0.27 and C = 0.20, we get:

200 * 0.27 + 150 * 0.20 + 100 * A ≥ 90
54 + 30 + 100 * A ≥ 90
A ≥ 6/100 = 0.06

Thus, the minimum value of A is 6%.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 08:16
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200 grams of pistachios would give 27% of fiber = 54 grams
150 grams of popcorn would give 20 % of fiber = 30 grams
100 grams of almonds would give 10% of fiber = 10 grams
Total = 54 + 30 + 10 = 94 grams

Lowest possible fiber percentage that pistachios can have be = 90 - fiber in 150 grams of popcorn - fiber in 100 grams of almonds
= 90 - 30 - 10 grams
= 50 grams which is 25% of 200 grams of pistachios

Lowest possible fiber percentage that almonds can have be = 90 - fiber in 200 grams of pistachios - fiber in 150 grams of popcorn
= 90 - 54 - 30 grams
= 06 grams which is 06% of 100 grams 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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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 08:23
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As per given conditions,

Fiber Goal: At least 90 grams from the snack.

Pistachios: 200 grams and its maximum fiber percentage: 27%

Popcorn: 150 grams and its maximum fiber percentage: 20%

Almonds: 100 grams and its maximum fiber percentage: 10%

Scenario 1: Lowest possible fiber percentage for Pistachios
To find the lowest possible fiber percentage for pistachios, we need to assume that popcorn and almonds contribute their maximum possible fiber. This way, pistachios have to "make up" the least amount of fiber to reach the 90-gram goal.

Max fiber from Popcorn = 150 grams * 20% = 150 * 0.20 = 30 grams

Max fiber from Almonds = 100 grams * 10% = 100 * 0.10 = 10 grams

Total max fiber (Popcorn + Almonds) = 30 grams + 10 grams = 40 grams

Minimum fiber from Pistachios = Fiber Goal - Total max fiber (Popcorn + Almonds) = 90 grams - 40 grams = 50 grams

lowest possible fiber percentage for Pistachios = (Minimum fiber from Pistachios / Weight of Pistachios) * 100% = (50 grams / 200 grams) * 100% = 0.25 * 100% = 25%

Scenario 2: Lowest possible fiber percentage for Almonds
To find the lowest possible fiber percentage for almonds, we need to assume that pistachios and popcorn contribute their maximum possible fiber. This way, almonds have to "make up" the least amount of fiber to reach the 90-gram goal.

Calculate maximum fiber from Pistachios = 200 grams * 27% = 200 * 0.27 = 54 grams

Calculate maximum fiber from Popcorn = 150 grams * 20% = 150 * 0.20 = 30 grams

Calculate total maximum fiber from Pistachios and Popcorn = 54 grams + 30 grams = 84 grams

Minimum fiber from Almonds = Fiber Goal - Total max fiber (Pistachios + Popcorn) = 90 grams - 84 grams = 6 grams

Lowest percentage for Almonds = (Minimum fiber from Almonds / Weight of Almonds) * 100% = (6 grams / 100 grams) * 100% = 0.06 * 100% = 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 08:24
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To minimize the fiber % in one nut while still hitting 90 g total, we max out the fiber from the other two:
  1. Pistachios
    • Max fiber from popcorn = 150 g × 20% = 30 g
    • Max fiber from almonds = 100 g × 10% = 10 g
    • Remaining needed = 90 g − (30 g + 10 g) = 50 g
    • So pistachio % greater than or equal to 50 g ÷ 200 g = 25%
    Lowest feasible pistachio fiber % = 25%.
  2. Almonds
    • Max fiber from pistachios = 200 g × 27% = 54 g
    • Max fiber from popcorn = 150 g × 20% = 30 g
    • Remaining needed = 90 g − (54 g + 30 g) = 6 g
    • So almond % greater than or equal to 6 g ÷ 100 g = 6%
    Lowest feasible almond fiber % = 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 04 Jul 2025, 08:50
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Information given:
- Arman's snack: 200g pistachios, 150g popcorn, 100g almonds
- He needs 90+ grams fiber in total
- Max fiber %: pistachios 27%, popcorn 20%, almonds 10%
- Goal: select lowest possible fiber % for pistachios and almonds that still allows him to reach 90 grams

Question:
- What's the lowest possible fiber % for pistachios and almonds that still allows Arman to hit his 90 grams fiber goal?

Solution:
- Total fiber needed: 90 grams
- Contribution: (200 * P) + (150 * C) + (100 * A)
- We want to minimize the fiber % for pistachios and almonds, so we have to maximize popcorn first

- Popcorn max: 20% of 150 grams, so 30 grams of fiber
- Since max popcorn gives 30 grams, we need 60 grams from pistachios and almonds

- Almonds max: 10% of 100 grams, 10 grams of fiber
- Remaining 50 grams must come from pistachios
- 50 grams / 200 grams = 25%
- So, pistachios must be at least 25%

- Pistachios max: 27% of 200 grams, 54 grams of fiber
- Remaining 6 grams must come from almonds
- 6 grams / 100 grams = 6%
- So, almonds must be at least 6%

Answer: Pistachios 25%, 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 04 Jul 2025, 08:52
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Setting max fiber limits for each

27% of 200gm Pistachio = 54gm
20% of 150gm Popcorn = 30gm
10% of 100gm Almond = 10gm
--------------------------------------
Add all we get total = 94gm

Since we only have a margin of 4 gms
The least we can go in any is to take 4gms from either of them

That makes either
2% less in Pistachio = 27-2 = 25%, or
2.66% less in Popcorn = 20-2.66 = 17.33%, or
4% less in Almond = 10-4 = 6%

From the choices
Final answer will be 25% for Pistachio and 6% for Almonds
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 08:53
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Arman needs 90 grams of fiber total from his snack mix of pistachios, popcorn, and almonds.
For the pistachios column:
* We assume popcorn has 20% fiber (its maximum) and almonds have 10% fiber (their maximum)
* This gives us 30g fiber from popcorn (20% of 150g) and 10g fiber from almonds (10% of 100g)
* So pistachios need to provide 90g - 40g = 50g of fiber
* Since there are 200g of pistachios, the percentage needed is 50g ÷ 200g = 25% For the almonds column:
* We assume pistachios have 27% fiber (their maximum) and popcom has 20% fiber (its maximum)
* This gives us 54g fiber from pistachios (27% of 200g) and 30g fiber from popcorn (20% of 150g)
* So almonds need to provide 90g - 84g = 6g of fiber
* Since there are 100g of almonds, the percentage needed is 6g = 100g = 6%
The answer is 25% for pistachios and 6% for almonds.
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 08:56
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Pistachios maximum = 27 percent
Popcorn maximum fibre = 20 percent
Almond maximum fibre = 10 percent .

Almond remains unchanged = 10 percent = 10 gms of fibre . 80 gms left.

Pistachios = 200 gms * 25 percent = 50 gms
Popcorn = 150 gms *20 percent = 30 gms.
Total 90 gms which has to be taken .
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 08:59
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For pistachios to minimize, lets have the popcorn and almonds maximize as much as possible (at max %).
Popcorn: 150g⋅20%= 30g
Almonds: 100g⋅10%=10g

So total from popcorn + almonds = 30 + 10 = 40g

Now pistachios must provide at least: 90g−40g=50g

Pistachios = 200g
We want the lowest % that gives ≥ 50g:
50/200=0.25=25%
So pistachios must be at least 25% fiber.

Similarly, solving for Almonds,
Let popcorn and pistachios contribute their maximum fiber:
Popcorn: 150g⋅20%=30g
Pistachios: 200g⋅27%=54g
Combined: 30+54=84g

So almonds must contribute: 90−84=6g
Almonds = 100g
We want the lowest % that gives ≥ 6g:
6/100=0.06=6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 09:02
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To find the lowest possible fiber percentage for each item (Pistachios and Almonds) while still meeting the 90-gram fiber goal, we must assume that the other snack components contribute their maximum possible fiber.

Here's the breakdown of the snack components and their maximum fiber contributions:

Pistachios: 200 grams, max fiber % = 27%

Popcorn: 150 grams, max fiber % = 20%

Almonds: 100 grams, max fiber % = 10%

The total fiber goal is at least 90 grams.

1. Calculate the lowest possible fiber percentage for Pistachios:

To minimize the fiber percentage required from pistachios, we assume popcorn and almonds contribute their maximum fiber:

Maximum fiber from Popcorn = 150 grams × 20% = 150 × 0.20 = 30 grams

Maximum fiber from Almonds = 100 grams × 10% = 100 × 0.10 = 10 grams

Total maximum fiber from Popcorn and Almonds = 30 grams + 10 grams = 40 grams.

Fiber still needed from Pistachios to reach the 90-gram goal = 90 grams - 40 grams = 50 grams.

Let P fiber% be the required fiber percentage for pistachios.
(200 grams) × P fiber% ≥50 grams
P fiber% ≥ 50/200
P fiber% ≥0.25

So, the lowest possible fiber percentage for pistachios is 25%.

2. Calculate the lowest possible fiber percentage for Almonds:

To minimize the fiber percentage required from almonds, we assume pistachios and popcorn contribute their maximum fiber:

Maximum fiber from Pistachios = 200 grams × 27% = 200 × 0.27 = 54 grams

Maximum fiber from Popcorn = 150 grams × 20% = 150 × 0.20 = 30 grams

Total maximum fiber from Pistachios and Popcorn = 54 grams + 30 grams = 84 grams.

Fiber still needed from Almonds to reach the 90-gram goal = 90 grams - 84 grams = 6 grams.

Let A fiber% be the required fiber percentage for almonds.
(100 grams) × A fiber% ≥6 grams

A fiber% ≥0.06

So, the lowest possible fiber percentage for almonds is 6%.

Based on the calculations, the selections are:
Pistachios: 25%
Almonds: 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 09:17
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IMO should be 25% for pistachios and 6% for almonds

The total fiber from the current contents and percentages is (Popcorn+Almonds+Pistachios)=(30+10+54)=94. If 90 is the minimum, the inly a reduction of 4 gms is possible.

For Almonds - 10-4 = 6 which is 6% of 100
For Pistachios - 54-4=50 which is 25% of 200

Thus, the chosen options
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 09:21
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So to find min of one we need max fibre from other two
27%, 20%, and 10%
For min pistachio => 90 - max fibre of (popcorn) - max fibre of (almonds)
90-20% of 150 - 10% of 100
90 - 30 -10 = 50 which is 25% of 200 so ans 25%

For min almonds => 90 - max fibre of (popcorn) - max fibre of (pistachio)
90-20% of 150-27% of 200
90-30-54 = 6 which is 6% of 100 so ans 6%
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 09:25
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WTF is this diet plan. I am going crazy to try to get 30 gms of fiber.
anyway.

Firstly we need to understand that we use max min ideas.

max out popcorn. 150gms at 20% will give 30 grams.

60 grams needed.
max almonds,
10% of 100 grams. = 10 grams

50 grams minimum needed from 200 grams pista

[50/200]*100= 25%


60 grams needed.
max pistas,
27% of 200 grams. = 54 grams

6 grams minimum needed from 100 grams almonds

[6/100]*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 04 Jul 2025, 09:25
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To get the lowest possible fiber percentage for pistachios,we must take the max fibre percentage from popcorn and almonds
So
x/100*200+20/100*150+10/100*100>=90
2x+30+10>=90
2x>=50
x>=25
So lowest possible fiber percentage for pistachios is 25 %

To get lowest possible fiber percentage that almonds,we must take the max fibre percentage from popcorn and pisitachios
27/100*200+20/100*150+x/100*100>=90
54+30+x>=90
x>=6
So lowest possible fiber percentage that almond is 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 04 Jul 2025, 09:26
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Ans: pistachios =25% and Almond = 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.

200 grams of pistachios with 27% fiber = 54 gm
150 grams of popcorn with 20% fiber = 30 gm
and 100 grams of almonds with 10% fiber = 10 gm
needs to meet 90 gm fiber

for minimum pistachios fiber %age in given snack weight
30+ 10 = 40 gms = 50 gms remaining which needs to be covered with 200 gm pistachios so 25% per 100gm would give 50gm from 200 gm
25% is the ans for pistachios

for minimum Almond fiber %age in given snack weight
54+ 30 = 84 gms = only 6 gm remaning which needs to be covered with 100 gm Almonds so 6% per 100gm would give 6 gm
6% is the ans for Almonds
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 09:30
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Pistachios = 200 grams have atmost 27% or 54 grams fibre
Pop corn= 150 grams have atmost 20% or 30 grams fibre
Almonds= 100 grams have atmost 10% or 10 grams fibre
His goal is atleast 90 grams of fibre

To minimise the percentage of Five in Pistachios, maximize fibre content in other two

the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal =90-30-10=50 grams
Percentage =50/200 *100=25 %

the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal = 90-54-30=6 grams
Percentage= 6/100*100=6 %
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 09:33
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Calculating the grams of fiber in each snack individually, we get

Pistachios 27% of 200 gms = 54 gms
Popcorn 20% of 150 gms = 30 gms
Almonds 10% of 100 gms = 10 gms

The lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal

Keeping 100% values for Popcorn (30 gms) and Almond (10 gms) we need 50 gms of Pistachios which is 25% of 200 gms

Keeping 100% values for Popcorn (30 gms) and Pistachios (54 gms) we need 6 gms of Almonds which is 6% of 100 gms


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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 04 Jul 2025, 09:35
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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.

so as to get 90 gms fiber leaving pistachios , diet has met 40 gms with almonds & popcorn
for rest 50 gms ; 50/200 * 100 = 25%

similarly for case ii of lowest possible fiber % of almonds ; 84 has been met by popcorn & pistachio
6/100 * 100 ; 6% by almond

25% & 6% is correct option
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GMAT Club Olympics 2025 (Day 5): Arman is tracking his fiber intake 04 Jul 2025, 09:39
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PistachioPopcornAlmonds
Quantity200150100
Max fiber %27%20%10%
Max fiber in g543010

Total required = 90

Calculating the max fiber % required for pistachio, we have popcorn + almonds contribute 40g
Max Fiber = 90-40=50g
Max Fiber % = 50/200 *100 = 25%


Calculating the max fiber % required for almonds, we have popcorn + pistachio contribute 84g
Max Fiber = 90-84=6g
Max Fiber % = 6/100 *100 = 6%

Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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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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