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The table above gives the number of calories and grams of

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The table above gives the number of calories and grams of  [#permalink]

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New post Updated on: 27 Dec 2018, 08:08
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Project DS Butler: Day 52: Data Sufficiency (DS104)


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Food -- Number of Calories per Kilogram -- Number of Grams of Protein per Kilogram
S ----- 2.000 -----------------------------------------150
T ----- 1,500 -----------------------------------------90

The table above gives the number of calories and grams of protein per kilogram of foods S and T. If a total of 7 kilograms of S and T are combined to make a certain food mixture, how many kilograms of food S are in the mixture?

(1) The mixture has a total of 12,000 calories.
(2) The mixture has a total of 810 grams of protein.

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Originally posted by boomtangboy on 01 Apr 2012, 04:26.
Last edited by gmatbusters on 27 Dec 2018, 08:08, edited 2 times in total.
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Re: The table above gives the number of calories and grams of  [#permalink]

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New post 01 Apr 2012, 07:15
3
Food -- Number of Calories per Kilogram -- Number of Grams of Protein per Kilogram
S ----- 2.000 -----------------------------------------150
T ----- 1,500 -----------------------------------------90

The table above gives the number of calories and grams of protein per kilogram of foods S and T. If a total of 7 kilograms of S and T are combined to make a certain food mixture, how many kilograms of food S are in the mixture?


(1) The mixture has a total of 12,000 calories --> say x kilograms of food S are in the mixture then there will be 7-x kilograms of food T in the mixture. Now, according to the table above we'll have: 2,000x+1,500(7-x)=12,000, since there is only one variable then we can solve for it. Sufficient.

(2) The mixture has a total of 810 grams of protein --> 150x+90(7-x)=810, since there is only one variable then we can solve for it. Sufficient.

Answer: D.
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Re: The table above gives the number of calories and grams of  [#permalink]

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New post 25 Jul 2012, 20:34
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1
boomtangboy wrote:
Food -- Number of Calories per Kilogram -- Number of Grams of Protein per Kilogram
S ----- 2.000 -----------------------------------------150
T ----- 1,500 -----------------------------------------90

The table above gives the number of calories and grams of protein per kilogram of foods S and T. If a total of 7 kilograms of S and T are combined to make a certain food mixture, how many kilograms of food S are in the mixture?

(1) The mixture has a total of 12,000 calories.
(2) The mixture has a total of 810 grams of protein.


Responding to a pm:

S -> 2000 C/kg and 150 P/kg
T -> 1500 C/kg and 90 P/kg

The mixture of the two is 7 kg.

Statement 1:
Mixture has 12000 C i.e. 12000/7 C/kg

The average calorie content of the mixture is 12000/7.

wT/wS = (AS - Aavg)/(Aavg - AT) (this formula represents the scale. You can either use the number line or this formula)

wT/wS = (2000 - 12000/7)/(12000/7 - 1500) = 2000/1500 = 4/3
So, in 7 kg, T was 4 kg and S was 3 kg

You don't really need to solve it. From the data you see that you have calorie content of each food and the average calorie content, so you can easily find the ratio of each food in the mixture. You also have the amount of mixture so you can easily find the amount of each food in the mixture.

Statement 2:
Mixture has 810 gms of P i.e. 810/7 P/kg

wT/wS = (150 - 810/7)/(810/7 - 90)

Again, same process as above.
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Re: The table above gives the number of calories and grams of  [#permalink]

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New post 15 Aug 2012, 11:46
Bunuel/ Karishma
Please let me know if this approach is ok
stmt 1
s+t = 7
2000s+1500T= 12000
solving for s , we get s is 3 and therefore sufficient

similiarly
s+t =7
150s +90 T= 810, solving for s, we get s = 3 and hence sufficient.
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Re: The table above gives the number of calories and grams of  [#permalink]

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New post 16 Aug 2012, 00:42
yogeshwar007 wrote:
Bunuel/ Karishma
Please let me know if this approach is ok
stmt 1
s+t = 7
2000s+1500T= 12000
solving for s , we get s is 3 and therefore sufficient

similiarly
s+t =7
150s +90 T= 810, solving for s, we get s = 3 and hence sufficient.


Your solution is correct. Notice that it's basically the same as my solution here: the-table-above-gives-the-number-of-calories-and-grams-of-129998.html#p1068312 You used two variables s and t (7-s), while I used x and 7-x.
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Re: The table above gives the number of calories and grams of  [#permalink]

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New post 13 Jun 2013, 01:16
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: The table above gives the number of calories and grams of  [#permalink]

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