Vegfood, a food wholesaler, plans to sell three different nut blends

Question

‎ ‎ ‎ ‎ ‎ ‎ Vegfood, a food wholesaler, plans to sell three different nut blends to grocery stores. Each blend will consist of two to four types of nuts and will be marketed in 300 gram (g) packages, each containing a total of 10 standard servings. Vegfood's plan stipulates that the blends should meet the following criteria:

1. The total price paid to suppliers for the ingredients of each blend must not exceed 50% of the blend's wholesale selling price.

2. Each blend's average nutritional profile per serving must comply with at least two of the following constraints for nutritional content:

‎ ‎ ‎ ‎ ‎ ‎ Carbohydrate: at most 10 g
‎ ‎ ‎ ‎ ‎ ‎ Protein: at least 5 g
‎ ‎ ‎ ‎ ‎ ‎ Dietary fiber: at least 4 g
‎ ‎ ‎ ‎ ‎ ‎ Saturated fat: at most 3 g

chetan2u · Accepted Answer

Plan :
10 servings of 30 gm each
Contain 2 to 4 types of nuts, with none amounting to more than 50% of total cost
AT least 2 of these to be maintained:  C\leq 10 , P\geq 5 , D\geq 4 , F\leq 3  
 Ratios 
Proportion of nuts in three types of blend is given

Nutrients 
Amount of nutrients in 30g of nuts is given

Q.1. Suppose the initial proposals from the Vegfood marketing department concerning proportions of nuts in the blends are followed. For each of the following, select Yes if it gives the weight of pecans that the information provided indicates would be, on average, in a 300 g package of the blend mentioned. Otherwise, select No.

Initial proposal is given under Ratios. Pecans are 0.1, 0.4 and 0.3 in 1 gm of Blend 1, 2 and 3 respectively.
For amount in 300g, multiply the amount by 300, so Pecans will be 0.1*300, 0.4*300 and 0.3*300 in 1*300 gm of Blend 1, 2 and 3 respectively.
 That is, 30g, 120g and 90g in Blend 1, 2 and 3 respectively. But the options are 10g, 40g and 90g resp.

So answer is No, No and Yes

Q.2. Suppose Vegfood, after a review of the marketing department's proposal for Blend 1, decided to reconfigure the blend by excluding almonds while making no changes to the 300 g package weight or to the ratios, by weight, among the other types of nuts. Given the information provided, which one of the following must then be true of the reconfigured blend?  
Blend 1 had 0.4 or 40% Almonds that will now get distributed in remaining nuts in the ratio of 0.2:0.1:0.3 or 2:1:3
 We can calculate each nutrient, which will be time consuming but scanning the graph would give us answer quickly.

(a) The blend's protein content is at least as much as that of the originally proposed Blend 1.
  Almond had 6g of protein. But after replacement, the proportion of protein in other nuts is below 6.  
Not true

(b) The blend violates the nutritional-profile condition for carbohydrate.
 C\leq 10 .
 If we look at carbohydrates column, the maximum is 9.6g in 30g in Cashew. Thus it would never be more than 9.6g 
Does not violate so not true

(c) The blend violates the nutritional-profile condition for dietary fiber.
 D\geq 4 .
 If we look at Dietary fibre column, the maximum is 4g in 30g of Almonds. But Almond is replaced with other nuts containing much lesser amount. Thus it would be lesser than 4g 
 Does violate, so true

We can check remaining two options too similarly. But we already have our answer above. 
(d) The blend violates the nutritional-profile condition for saturated fat.
(e) The blend's saturated-fat content derived from walnuts is no greater than that of the originally proposed Blend 1.

Q.3. Suppose Blend 2 complies with the initial proposals of Vegfood's marketing department. For each of the statements concerning average nutritional content of a 30 g serving of Blend 2, select Yes if the information provided indicates that the statement is correct. Otherwise, select No.  
Scan the graph again.
(a) The highest possible proportion of carbohydrate is 9.6g,  so it is always less than 10g...Yes 
(b) The highest possible proportion of protein is 6g, so it would be 6g, if it contained only almonds. But other nuts have lesser proportion,  so overall it is always less than 6g....Yes 
(c) The highest possible proportion of dietary fibre is 4g, so it would be 4g, if it contained only almonds. But other nuts have lesser proportion,  so overall it is always less than 4g....Yes

SergejK · Answer

I feel to answer this question one must understand the process of storing information while reading all the information provided in the tabs and the needed inferences to understand what possible questions could be.

Looking at the  'Plan'  tab, we should just see that there are  constraints  presented. Reading Goal: know where the constraints are, don't have to understand them 100% at first.

Reading the tab  'Ratios'  we need to see that those numbers within the table are  proportions . Firstly, the text above explains that those are proportions. Secondly, looking at the numbers, we should use our number sense and realize that together each blend adds up to 1 or 100%. Using pre-thinking, we should understand that we will probably need to use those proportions on something. Combining this information with the 'Plan' tab we should see that a possible connection could be the constraints regarding nutrients. IMPORTANT: as MAX price per kg for each nut is not yet mentioned, just park the information and know that it is provided for each nut category. Could be important for one of the questions.

This understanding leads us logically to the  'Nutrients'  tab. Now, from the 'Plan' tab we know that each blend will consist of 300g packages. In the 'Nutrients' tab we are told what the nutrients values are for each of the 4 nut types of a 30g serving, so just 1/10th of the total package. DIFFICULTY: the graph is arranged according to nutrients and not nuts, so logically, we must understand that the arrangement doesn't change anything: for each nut type, a specific gram value of nutrients is provided, NOT PERCENT!!! So the last connection that we must create is the 'Ratios' tab, where proportions are provided as % of the respective nut types, hence, a multiplication of proportions with the respective grams of the nutrients will let us know the amount of the nutrients in each blend.

For me this was a very tough question. But I feel that connecting each tab logically, helps to understand possible question that may arise and this inference should help answer them.

Thaania · Answer

Could you please explain Q.2 and 3? Thanks in advance!

SergejK · Answer

Q2 just requires you to understand the data that is provided. In the Plan tab under point 2. the AVERAGE nutritional profile per serving CONSTRAINTS are presented. Additionally, under Ratios tab the proportions without almonds need to be calculated, ONLY if we really need them. However, looking at the answer choices and the tab Nutrients, we see that such lengthy calculation in Blend1 can maybe be left out, if we can spot right away whether the constraints are not met or the averages changed. This question requires you to understand how averages work. If almonds are removed, the average will only go up, if almonds would have provided the least amount of nutrients in a serving. Conversely, the average will go down if the almonds would have provided the highest amount of nutrients in a serving. In our case, only carbohydrates would require calculation if we are asked for the averages as we would then need to check whether our new proportions in the Ratio tab without almonds would change the average. We also can just assume that in carbohydrates, just because almonds are higher than the average, removing those would lower the average, as we don't know (without further calculations) whether the over proportional distribution of the highest data points would raise the average or the over proportional distribution of the lowest data points would lower the average.

A.  The blend's protein content is at least as much as that of the originally proposed Blend 1. => This cannot be true as the almonds have provided the highest amount of proteins. Removing them would lead to a lower average of protein in the serving. 
 B. The blend violates the nutritional-profile condition for carbohydrate. => As we are asked not for the average but whether removing almond would violate the constraints, we see that the constraint in the Plan tab is a max of 10g. With or without almonds those constraints are not violated as for the averages to be above 10g at least one nut type should provide >10g, which is not the case in carbohydrates, hence B is wrong. AND: no calculation is needed. 
   C.     The blend violates the nutritional-profile condition for dietary fiber.  => So the constraint for dietary fiber is an average of >4g per 30g. Looking at the Nutrients tab we see that even with almonds, the average will be lower than 4, so this is correct. 
D. The blend violates the nutritional-profile condition for saturated fat. => Wrong, as our constraints tell us that saturated fat must have an average of <=3g. Looking at the Nutrients tab we see that even with almonds this constraint is not violated. 
E. The blend's saturated-fat content derived from walnuts is no greater than that of the originally proposed Blend 1. => This is clearly wrong as prior to removing almonds from Blend 1, the saturated fat content from walnuts was 3/10 of the serving. When we remove the almond we are told to make no changes to the ratios. Our new saturated fat content from walnuts becomes now 3/6, which is clearly larger than 3/10.

SergejK · Answer

Q3 is along the lines of Q2. We are asked for the average nutritional content of a 30 g serving of Blend 2, assuming it complies with the initial proposals of Vegfood's marketing department.

Its carbohydrate content is less than 10 g. => must be less than 10 as no one nut type is above 10g

Its protein content is less than 6 g. => must be less than 6 as no one nut type is above 6g

Its dietary fiber content is less than 4 g. => must be less than 4 as no one nut type is above 4g

shashank07! · Answer

hi  chetan2u  , can you please explain the second one with calculations in my case, the 3rd case was not getting violated

samarpan.g28 · Answer

We need at least 4g of Dietary Fibre.

If the entire 30gms serving consisted of Almonds then we could have said that it satisfies the nutritional-profile condition. But having Almonds out of the scene, no matter how much in quantity the other nuts we add, the total Dietary Fibre content can never match the minimum 4 grams as asked in requirements.

From the second tab, we can calculate Blend 1 could have 12gms of Almonds, 6gms of cashews, 3gms of Peacans and 9gms of Walnuts. We remove the Almonds.

Tab 3 gives how much nutrition each nut will have for their 30gms serving.

in Blend 1,
 
Dietary Fibre content of Cashew is ((1.1 * 6)/30) = 0.22gms
Peacans will have ((2.5 * 3)/30) = 0.25gms
Walnuts will have ((2.5 * 9)/30) = 0.75gms

They add up to 1.22gms of Dietary Fiber (less than 4gms) so it violates the nutritional-profile condition.

I hope this helps.

Rongoing · Answer

I think Q2&3 need to be done with the ratio.
nutrients tab shows important nutritional contents for a 30 g serving of  each of the four types  of nuts, which means, for example, 30g almonds has 6g carbohydrates, and when we talk to the carbohydrates in blend 1, it should be 0.4✖6+0.2✖9.6+0.1✖3.8+0.3✖3.8. Is it right?

GMAT1034 · Answer

Hi, for the 3rd question why are we taking just 1 nut's carbohydrate content into consideration. The question says each blend would have 2-4 types of Nuts. Am I missing something here?
 Bunuel   MartyMurray   GMATNinja   KarishmaB

cheshire · Answer

We are taking blend 2, which has 3 nuts. If we were to calculate the nutritional content based on the ratio of each nut in mix, all the answers would be no. And honestly you don't even need to calculate it, as the thresholds are easy to compare with the data.

RudreshKal · Answer

can you please explain  Q2 again. i think it violates Saturted Fats as well

blend 1 = 300g ( almods 120, c 60, p 30, w 90) 
 new blend 1 = 300g (c 100, p 50, w 150)

if we add cumultive nos from per 30g servings, we will get more 3g for sturted fats or have i made mistk in per servings concept?

Bunuel · Answer

No, it doesn’t violate saturated fat. The confusion comes from adding the full 30 g nutrient values for each nut instead of weighting them. In the 30 g serving of the new blend, only 10 g are cashews, 5 g pecans, and 15 g walnuts. When you apply those proportions, the saturated fat total is about 2.2 g, still under the 3 g limit.

Usernamevisible · Answer

KarishmaB  - it would be great to see your youtube video on this

KarishmaB · Answer

Thanks for the shoutout Usernamevisible . I will get to it though not sure by what time

MinhHoang31 · Answer

here is my reasoning for this question
 QUESTION ANALYSIS 
This question tests your knowledge on Weighted Average
Tab2 shows the proportions by weight for each type of nut in a blend
Tab3 shows the nutrient content in a 30g serving of each type of nut

Let's think that this question asks us to calculate the exact value to validate each statement, for example we need to find the exact nutrient value for Fiber in a standard serving of Blend 1, this is equal to:
(Fiber per gram of A x amount of A in one serving) + (the same for other nuts)
Fiber per gram of A = Fibers in 30g of A / 30
Amount of A in one serving = 30 x proportion of A

Substitute those equivalences into the formula, it then becomes:
(Fiber in 30g of A x proportion of A) + (fiber in 30g of C x proportion of C) + (Fiber in 30g of P x proportion of P) + (Fiber in 30g of W x proportion of W)
The sum of those proportions are always equal to 1

EXAMINE THE STATEMENTS 
This is weighted average formula and we know that a weighted average always lands between the lowest and highest values in the mix. That's why we can validate each statement without much calculations as below:
 Statement 1: the blend's protein content is at least as much as that of the originally proposed Blend 1 
We remove Almond as the one with the highest "protein rate", so the protein content now per serving of blend 1 must be less than before, and thus the total content of protein for the whole blend must also be less than before -> False

Statement 2: The blend violates the nutritional-profile condition for carbohydrate 
From tab1: we know that the content for C per serving must be at most 10
We know that the C content per serving must between 3.8 and 9.6 based on tab2. so after removing, this content still doesn't violate the rule -> False

Statement 3: The blend violates the nutritional-profile condition for dietary fiber 
From tab 1: we know that the content for F per serving must be at least 4
After removing almonds, minFiber = 1.1 and new maxFiber = 2.5 -> the new content for P must between 1.1 and 2.5, exclusively -> Correct

Statement 4: The blend violates the nutritional-profile condition for saturated fat 
From tab1: we know that the content for F per serving must be at most 3g
After removing almonds, minF = 1.9 and maxF = 2.7 - the new content for F must be between 1.9 and 2.7 -> doesn't violate the contraint -> False

Statement 5: The blend's saturated-fat content derived from walnuts is no greater than that of the originailly proposed blend 1 
We know that after removing almonds, we need to increase each of the remaining 3 nuts proportionally so they can add up to 300g, that means we need a higher amount of walnuts and thus a higher amount of Fat provided by Walnut than the originally proposed Blend 1

So the correct answer is statement 3

Yes	No
		Blend 1: 10 g of pecans
		Blend 2: 40 g of pecans
		Blend 3: 90 g of pecans

Vegfood, a food wholesaler, plans to sell three different nut blends

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	The blend's protein content is at least as much as that of the originally proposed Blend 1.
	The blend violates the nutritional-profile condition for carbohydrate.
	The blend violates the nutritional-profile condition for dietary fiber.
	The blend violates the nutritional-profile condition for saturated fat.
	The blend's saturated-fat content derived from walnuts is no greater than that of the originally proposed Blend 1.

Yes	No
		Its carbohydrate content is less than 10 g.
		Its protein content is less than 6 g.
		Its dietary fiber content is less than 4 g.

GMAT Multi-Source Reasoning (MSR) Questions

Vegfood, a food wholesaler, plans to sell three different nut blends

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615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards