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

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04 Jul 2025, 09:41

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Bunuel

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Solving pistachios fibre is 27/100*200=54grams
popcorn fibre is 20/100*150=30grams
Almonds fibre is 10/100*100=10 grams
Total=94 grams the lowest for pistachios is 94-90=4 hence 54-4=50 therefore 50 grams is 25%
Lowest for almonds is 10-4= 6 hence 6%

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04 Jul 2025, 09:41

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PISTA:
(p*200)+(150*0.2)+(100*0.1)=90
p=0.25...25%

Almonds:
(200*0.27)+(150*0.2)+(100*a)=90
a=0.06..6%

Ans 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.

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

Total fiber in mid-days snacks = 54 + 30 + 10 = 94 grams

Pistachios the lowest possible fiber percentage that pistachios can have

200*x% + 30 + 10 >=90
2x >=50
x >= 25

Almonds the lowest possible fiber percentage that almonds can have

54 + 30 + z >=90
z >= 6

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
25	6

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04 Jul 2025, 09:46

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Max contents:
Pistachio(P)= 27% of 200gm = 54gm
Almonds (A)= 10% of 100 gm= 10gm
Pop-corn (PC)= 20% of 150gm= 30gm

Total Requirement is 90 gm

Min P= Total - max A -max PC = 90-10-30= 50 gm= 25% of 200

Min A= Total- max P - max PC= 90-54-30= 6 gm= 6% of 100

Answe: 25%, 6%

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04 Jul 2025, 09:51

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The quantity is given as:

Pista = 200g
Popcorn = 150g
Almonds = 100g

Maximum %ages of fiber
Pista = 27%
Popcorn = 20%
Almonds = 10%

Total fiber requirement = 90g

We need to find the lowest possible fiber percentage for both pista and almonds, such that our total requirement of 90g is met

For Pista:

To minimize the % contribution of fiber from pista, we have to maximize the % contribution from the other 2

Max fiber (in g) from popcorn and almonds = (max % of fiber in popcorn)*(quantity of popcorn) + (max % of fiber in almonds)*(quantity of almonds)
We get, max fiber (in g ) from popcorn and almonds = (20% of 10)+(10% of 100) = 40g

Now are requirement is for 90g, thus the 50g deficit is going to come from Pista:

Max % fiber from pista = (Deficit to be filled by pista)/(quantity of pista) = 50/200 = 25%

Similarly for almonds, we maximize the fiber from popcorn and pista first,

Max fiber (in g) from popcorn and pista = (max % of fiber in popcorn)*(quantity of popcorn) + (max % of fiber in pista)*(quantity of pisa)

We get, max fiber (in g) from popcorn and pista = (20% of 150)+(27% of 200) = 84g

Our requirement is 90g, so the deficit that's going to come from almonds is 6g

Max % fiber from almonds = (Deficit to be filled by almonds)/(quantity of almonds) = 6/100 = 6%

So the answer is,
Pistachio = 25%
Almonds = 6%

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04 Jul 2025, 09:54

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Given the info, maximum we can have 54gm, 30gm, 10gm for pistachios, popcorn, and almonds respectively
Now total has to be 90gm but 54gm, 30gm, 10gm add up to more than 90gm

To minimize pistachios, we can maximize popcorn and almonds which together is 40gm. Min pistochio will be 50gm, thus, lowest possible percentage is 50/200 = 25%

To minimize almonds, we can maximize popcorn and pistachios which together is 84gm. Min almonds will be 6gm, thus, lowest possible percentage is 6/100 = 6%

Hence, answer is (25%, 6%).

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04 Jul 2025, 09:57

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Bunuel

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The grams of fibre from each is
pistachios = 27% of 200 = 54 grams
popcorn. = 20% of 150 = 30 grams
almonds = 10% of 100. = 10 grams

So total = 94 grams

Hence the reduction of 4 grams of pistachios or almonds we yield:
pistachios = 50 grams/ 200 *100 = 25% Answer
almonds = 6 grams /100 * 100 = 6% Answer

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04 Jul 2025, 10:01

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Bunuel

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So the total needed fiber is 90g.

To select the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal, Possible only when Almonda and Pop are highest. So 200(p%) +30+10 = 90 => So p% = 25%

Similarly, for the lowest fiber for almonds.

54 + 30 + a%(100) = 90 => a=6%.

Hence IMO p = 25%, a = 6%

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04 Jul 2025, 10:14

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The problem requires finding the lowest possible fiber percentages for pistachios and almonds while ensuring the total fiber intake from the snack is at least 90 grams. The total fiber is the sum of the fiber from 200g of pistachios, 150g of popcorn, and 100g of almonds. This relationship can be expressed with the inequality: (200 * P_p) + (150 * P_c) + (100 * P_a) >= 90, where P_p, P_c, and P_a are the respective fiber percentages. The maximum fiber percentages are given as 27% for pistachios, 20% for popcorn, and 10% for almonds.

To find the lowest possible fiber percentage for pistachios, the contribution from the other two ingredients must be maximized. Using the maximum percentages for popcorn (20%) and almonds (10%), their combined fiber contribution is (150 * 0.20) + (100 * 0.10) = 30 + 10 = 40 grams. To meet the 90-gram goal, the pistachios must provide at least 90 - 40 = 50 grams of fiber. The lowest percentage for pistachios is therefore 50g / 200g = 0.25, or 25%.

To find the lowest possible fiber percentage for almonds, the contribution from pistachios and popcorn must be maximized. Using the maximum percentages for pistachios (27%) and popcorn (20%), their combined fiber contribution is (200 * 0.27) + (150 * 0.20) = 54 + 30 = 84 grams. To meet the 90-gram goal, the almonds must provide at least 90 - 84 = 6 grams of fiber. The lowest percentage for almonds is therefore 6g / 100g = 0.06, or 6%.

The lowest possible fiber percentage for pistachios is 25%, and the lowest possible fiber percentage for almonds is 6%.

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04 Jul 2025, 10:15

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so I am a bit unsure but posting what I think is the answer. I am considering the min % for each by considering that the other two should meet the rest required nutrition gap to 90gm. So for Pistachio is => 90 - (150 x 0.20 + 100 x 0.10) = 90 -40 = 50 gm. thus min % pistachio = 50/200 x100 = 25%. Similarly for Almonds => 6/100 X 100 = 6% Hope its correct, and if not then suggestions are welcome!

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04 Jul 2025, 10:17

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Given information:
Pistachios(Pt)= 200gm
Popcorn(Pp)= 150 gm
Almond(A)= 100gm

Total fiber required = 90gms

Maximum fiber in Pt=27%, Pp=20%, A=10%

Calculating the Maximum fiber in the snacks:
Pt: 27%*200= 54
Pp: 20%*150= 30
A: 10%*100= 10

Total= 54+30+10= 94
Extra fiber than required= 94-90= 4

Minimum amount of fiber in Pt can be: 54-4= 50
In %: x%*200=50
x=25% , which is the 5th option.

Minimum amount fiber in A can be: 10-4= 6
In %:y%*100=6
y=6% , which is the 3rd option.

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04 Jul 2025, 10:24

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Let x be percentage of fiber in Pistachio
y be percentage of fiber in Popcorn
z be percentage of fiber in Almonds

To minimize % in Pistachio, we need to maximize in both almonds and Popcorn
Maximum fiber in popcorn = 20% of 150 = 30g
Maximum fiber in Almonds = 10% of 100 = 10g
So minimum amount of fiber in Pistachio = 90-40 = 50g
in % terms = 50/200 * 100 = 25%

To minimize % in Almonds, we need to maximize in both Pistachio and Popcorn
Maximum fiber in popcorn = 20% of 150 = 30g
Maximum fiber in pistachio = 27% of 200 = 54g
So minimum amount of fiber in Pistachio = 90-84 = 6g
in % terms = 6/100 * 100 = 6%

Hence minimum % that pistachio can have is 25%
minimum % that almonds can have is 6%

Bunuel

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04 Jul 2025, 10:27

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Pistachio = 200g and 27% i.e. 54g fiber
Popcorn = 150g and 20% i.e. 30g fiber
Almond = 100g and 10% i.e. 10g fiber

Now, we need atleast 90g with Minimum Pistachio % - we can take 50g instead of 54 to make 90. Therefore 25% of 200
2) we need atleast 90g with Minimum almond % - we can take 6g instead of 10 to make 90. Therefore 6% of 100

Bunuel

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04 Jul 2025, 10:27

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Given,
For pistachio ---> Quantity = 200gms and max fiber = 27%
For popcorn---> Quantity = 150gms and max fiber = 20%
For almond---> Quantity = 100gms and max fiber = 10%

1.)Pistachios the lowest possible fiber percentage that pistachios can have while still meeting the 90-gram fiber goal.
For lowest value for pistachio, fiber content in popcorn and almond is to be max, hence
90=P%*200+20%*150+10%*100, therefore P = 25%

2.)Almonds the lowest possible fiber percentage that almonds can have while still meeting the 90-gram fiber goal.
For lowest value for almonds, fiber content in pistachio and popcorn is to be max, hence
90=27%*200+20%*150+P%*100, therefore P = 6%

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04 Jul 2025, 10:53

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Bunuel

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Min % from Pistachios

0.2 * 150 = 30
0.10 * 100 = 10

Total fibre = 40

Remaining = 90 - 40 = 50

50/200 * 100 = 20%

Min % from Almonds

0.27 * 200 = 54
0.20 * 150 = 30

Total fibre = 84

Remaining = 90 - 84 = 6

6/100 * 100 = 6%

Answer

Pistachios = 20%
Almonds = 6%

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04 Jul 2025, 10:54

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The way I solved this was by
1. Keeping maximum fiber percent for almonds and popcorn and x% for pistachio. Ultimately, all the fiber intake would add upto 90 grams.
((x/100)*200))+((20/100)*150)+((10/100)*100)=90
Based on this, when we solve for x, we get 25%.

2. Similarly, in the second one, we would keep maximum fiber intake for pistachio and popcorn and x% for almonds.
After making the equation for that, we will get =6%

Therefore, the answer is E C

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04 Jul 2025, 11:02

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To minimize one number, we should maximize the other ones.

Minimize pistachios:
Popcorn = 20% -> 20% of 150g = 30g
Almonds = 10% -> 10% of 100g = 10g
Pistachios need to contribute with 90g - 40g =50 g. Pistachios = 25%.

Minimize Almonds:
Pistachio = 27% -> 27% of 200g = 54g
Popcorn = 20% -> 20% of 150g = 30g
Almonds should contribute with 90g - 84g =6 g. Almonds = 6%.

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04 Jul 2025, 11:35

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Here is the explanation:

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.

Pistah	Popcorn	Almond	Total fiber required
200	150	100	90 grams

Since we need to minimize Pistah and Almond, let's maximize Popcorn
Max extraction from Popcorn at 20% of 150 is 30 grams
Balance 60 grams should be met by Pistah and Almond
Maximum Pistah can offer is 27% of 200 which is 54 grams
Balance 6 grams should come from almond, 6 grams is 6% of 100 grams of almond.

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04 Jul 2025, 11:39

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Pist=200g
pop=150g
A=100g
Fibre needed=F=90g
Max F % in Pist=27%=27/100*200=54g
Max F % in Pop=20%=1/5*150=30g
Max F % in A=10%=1/10*100=10g
Let the fiber from pist be 200×Fp
(200×Fp)+30+10>=90
200×Fp+40>=90
200×Fp>=50
Fp>=200
50Fp≥0.25
Let the fiber from almonds be 100F
54+30+(100F)>=90
84+100F>=90
100F>=6
F >=100
6F>=0.06

Pist:25, A:6

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04 Jul 2025, 11:49

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Bunuel

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Midday snack consists of 200 grams Pistachios, 150 grams popcorn and 100 grams Almonds.

We need Atleast 90 grams of fiber to meet nutritional goal ?

The maximum fibre percentages in Pistachios , Popcorn and Almonds are 27%, 20% and 10% respectively.

Lowest possible fiber percentage that Pistachios can have still meeting 90 gram fibre goal is ?

Popcorn = 20%*(150) = 30 grams

Almonds = 10%*100 = 10 grams

Totally 40 grams , remaining gram needed is 50.

What percent of 200 = 50 ? The answer is 25%.

Lowest possible fiber percentage that Almonds can still have meeting 90 gram fibre goal ?

Pistachios= 27%*200 = 54 grams

Popcorn = 20%*150 = 30 grams

Total fibre = 54+30 = 84 grams. To meet the fibre goal we need 6 grams from Almond.

6%*(100) = 6 grams.

Thus the lowest possible fiber percentage = 6 %. The answer is 6%