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Updated on: 01 Oct 2022, 08:18
Originally posted by boomtangboy on 01 Apr 2012, 04:26.
Last edited by Bunuel on 01 Oct 2022, 08:18, edited 4 times in total.
Last edited by Bunuel on 01 Oct 2022, 08:18, edited 4 times in total.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
Attachment:
2022-10-01_20-17-06.png [ 24.24 KiB | Viewed 16112 times ]
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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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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General Discussion
boomtangboy
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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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.
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.
yogeshwar007
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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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.
Let S be the weight of food S and T be the weight of food T.
We know from the stem that S + 7 = 7.
This statement tells us that 2000S + 1500T = 12000.
Since we have two unknown variables and two equations, we can solve.
Sufficient.
(2) The mixture has a total of 810 grams of protein.
Exact same logic as A.
150S + 90T = 810
S + T = 7
Solve for S.
Sufficient.
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.
Let S be the weight of food S and T be the weight of food T.
We know from the stem that S + 7 = 7.
This statement tells us that 2000S + 1500T = 12000.
Since we have two unknown variables and two equations, we can solve.
Sufficient.
(2) The mixture has a total of 810 grams of protein.
Exact same logic as A.
150S + 90T = 810
S + T = 7
Solve for S.
Sufficient.
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.
(1) What about if 6s + 0T = 6*2000 = 12000 or 0S + 8T = 12000 or even 3S + 4T = 12000
(2) What about if 0S + 9T = 810 or 3S + 4T = 810
Because It says "a misture", there will be always some portion of each?
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.
(1) What about if 6s + 0T = 6*2000 = 12000 or 0S + 8T = 12000 or even 3S + 4T = 12000
(2) What about if 0S + 9T = 810 or 3S + 4T = 810
Because It says "a misture", there will be always some portion of each?
zacheu
Dear zacheu,
you are right, the mixture is supposed to consist of at least two substances or ingredients.
Another point, you statement below is not fair
(1) What about if 6s + 0T = 6*2000 = 12000 or 0S + 8T = 12000 or even 3S + 4T = 12000
Take into consideration requirement from task stem:
If a total of 7 kilograms of S and T are combined to make a certain food mixture....
Thus, you ought to consider 7s + 0T = 7*2000 = 14000 - that is more than necessary.
The same valid for the your other statements.
Hope it helps
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Expert reply
Video solution (2:46):
Key Habit: Ideally we do NOT want to do any of these calculations; if we fully understand the concept, we'll realize that we have enough info to solve. I show approximate numbers here just for illustration.
Teeter Totter Basic Examples Playlist: https://www.youtube.com/playlist?list=PL2exXfCUscn8Hvafet5-IPH1eNNLSjQBP
_________________
Key Habit: Ideally we do NOT want to do any of these calculations; if we fully understand the concept, we'll realize that we have enough info to solve. I show approximate numbers here just for illustration.
Teeter Totter Basic Examples Playlist: https://www.youtube.com/playlist?list=PL2exXfCUscn8Hvafet5-IPH1eNNLSjQBP
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