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

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LastHero

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05 Jul 2025, 06:08

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If popcorn and almonds are at their maximum percentages, pistachios can be at its minimum percentage:
90 * 100 = 200*p + 150*20 + 100*10
90 = 2p + 15*2 + 10 = 40 + 2p
2p = 50
p = 25%

If pistachios and popcorn are at their maximum percentages, almonds can be at its minimum percentage:
90 * 100 = 200*27 + 150*20 + 100*a
90 = 54 + 15*2 + a = 84 + a
a = 6 %

Pistachios 25% and Almonds 6%

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05 Jul 2025, 06:23

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200g pistachios (max 27% fiber)
150g popcorn (max 20% fiber)
100g almonds (max 10% fiber)

Objective: Total ≥ 90g of fiber

1. The lowest possible fiber % for pistachios
To get this Max fiber from almond and popcorn

=>
Max fiber from popcorn = 150g × 20% = 30g
Max fiber from almonds = 100g × 10% = 10g
Required fiber from pistachio = 90 - (30+10) = 50g

Pistachio fiber % = 50/200 = 25% is the lowest possible fiber % for pistachios

2. The lowest possible fiber % for almonds
To get this Max fiber from pistachio and popcorn

=>
Max fiber from popcorn = 150g × 20% = 30g
Max fiber from pistachios = 200g × 27% = 54g
Required fiber from almonds = 90 - (30+54) = 6g

Almonds fiber % = 6/100 = 6% is the lowest possible fiber % for almonds

Pistachios: 25%
Almonds: 6%

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To meet the 90-gram fiber goal, the total fiber from pistachios, popcorn, and almonds must be at least 90 grams.
Popcorn contributes a fixed 30 grams (150g × 20%).
Setting almonds at their maximum fiber (10%) minimizes the pistachio fiber needed: solving 200P + 10 greater than or equal to 60 gives P greater than or equal to 25%.

Conversely, setting pistachios at their maximum (27%) minimizes almond fiber: solving 54 + 100A greater than or equal to 60 gives A greater than or equal to 6%.
Therefore, the lowest possible fiber percentages are 25% for pistachios and 6% for almonds.

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To find lowest fiber % for Pistachio, we need to maximise the percentages for almond and popcorn
Max % of almond = 10%, max quantity of fiber = 0.1*100 = 10
Max % of popcorn = 20, max quantity of fiber = 0.2*150 = 30

Remaining fiber = 90 - 40 = 50 gms.
Lowest fiber % = 50/200 * 100 % = 25%

Chose 25% for Pistachio

To find lowest fiber % for Almond, we need to maximise the percentages for pistachio and popcorn
Max % of pistachio = 27%, max quantity of fiber = 0.27*200 = 54
Max % of popcorn = 20, max quantity of fiber = 0.2*150 = 30

Remaining fiber = 90 - 84 = 6 gms.
Lowest fiber % = 6/100 * 100 % = 6%

Chose 6% for Almond

UfuomaOh

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Total fibre in

Pistachios : 27%* 200 = 54
Popcorn: 20% *150 =30
Almond: 10% * 100= 10
Total fiber 94

He needs 90

Lowest fiber percentage from

Pistachios = 90-30-10
= 50
50 is 25% of 200

Almons

90-54-30=6

6 is 6% of 100

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Bunuel

This question was provided by GMAT Club
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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, in this case we just have to keep in mind to maximize the other two options.
Meaning, that for the first case, we are talking about:

10%*100+ 20%*150+ X%*200 = 90
X = 25%

Same with the second option as well.

The result is:
1. 25%
And
2. 6%

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Bunuel

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Fiber needed = 90 gm,

Maximum fiber
Pist. = 200*27%= 54 gm, Popcorn = 150*20% = 30 gm , Almonds = 100*10% = 10 gms.

1. Lowest possible fiber percentage for Pistachios => when popcorn and almonds fiber %age is maximum.
Fiber needed=max. of Almond and popcorn + lowest possible of Pist.
90=30+10+ fiber from Pist.
fiber from Pist.= 50.
percentage = (50/200)*100= 25%

2. Similarly, 90 gm= 30+54 +y {Maximum fiber from Pist. and pop}
y=6
percentage = (6/100)*100 = 6%

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05 Jul 2025, 07:27

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

To still hit the goal of $90$g, we have a $4$g leeway.

Almonds can stay at $10$% but if pistachios drop to $25$%, then we can still maintain $90$g of fiber. But these two are not options.

Almonds can drop to $6$% and pistachios can stay at $27$%. This decreases the original fiber count by $4$g, which is exactly what we needed.

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To minimize Pistachios fiber percentage, we maximize fiber % of Popcorn & Almond: 30 + 10 = 40g
- Hence, we need at the min 50g of fiber from Pistachios -> 50/200g = 25%

To minimize Almond fiber percentage, we maximize fiber % of Pistachios & Popcorn: 54 + 30 = 84g
- Hence, we need at the min 6g of fiber from Almond -> 6/100 = 6%

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Pistachio: 200 grams
Popcorn: 150 grams
Almonds: 100 grams

To get lowest fiber percentage of pistachio:
200*x + 150*(max possible for popcorn) + 100*(max possible for almond) = 90
x= 25%

To get lowest fiber percentage of almond:
200*0.27 + 150*0.2 + 100x = 90
x = 6%

Pistachio: 26%
Almond: 6%

Bunuel

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If all the other products have maximum fiber percentages, percentage of pistachios can be minimum
20% of 150 grams of popcorn are 30 grams
10% of 100 grams of almonds are 10 grams
total = 90
90-30-10=50

PercentagePistachios * 200 = 50
PercentagePistachios = 25%

If all the other products have maximum fiber percentages, percentage of almonds can be minimum
27% of 200 grams of pistachios are 54 grams
20% of 150 grams of popcorn are 30 grams
total=90

90-54-30=6

PercentageAlmonds * 100 = 6
PercentagePistachios = 6%

PercentagePistachios = 25% and PercentagePistachios = 6%

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To get minimum percentage of pistachios we get maximum percentage of popcorn and almonds

200*pistachios/100 + 150*20/100 + 100*10/100 = 90
2*pistachios = 50
pistachios = 25%

To get minimum percentage of almonds we get maximum percentage of pistachios and popcorn
200*27/100 + 150*20/100 + 100*almonds/100 = 90
54 + 30 + almonds = 90
almonds = 6%

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Given: Pistachios (200g), Popcorn (150g), Almonds (100g); Max fiber%: Pistachios 27%, Popcorn 20%, Almonds 10%;
Goal: ≥90g fiber.

Assume Popcorn at max: 150 × 0.20 = 30g → Remaining needed = 60g

Let Pistachio % = x, Almond % = y → Equation: 200x + 100y = 60 → 2x + y = 0.6
For Pistachios min %: Set y = 0.10 → 2x = 0.5 → x = 25%
For Almonds min %: Set x = 0.27 → y = 0.6 − 0.54 = 6%

Final Answers: Lowest possible fiber % in Pistachios = 25% & Almonds = 6%.

Bunuel

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05 Jul 2025, 08:20

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For Pistachios:

Max fiber from Popcorn: 150*20% = 30g
Max fiber from Almonds: 100*10% = 10g
Total max from Popcorn & Almonds: 30+10 = 40g
Fiber needed from Pistachios: 90 - 40 = 50g
Lowest %age for Pistachios: (50/200)*100% = 25%

For Almonds:

Max fiber from Pistachios: 200g*27% = 54g
Max fiber from Popcorn: 150g*20% = 30g
Total max from Pistachios & Popcorn: 54+30 = 84g
Fiber needed from Almonds: 90(goal) - 84 = 6g
Lowest percentage for Almonds: (6g /100g)*100% = 6%

Bunuel

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