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The table above gives the number of calories and grams of pr

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The table above gives the number of calories and grams of pr [#permalink] New post 15 Mar 2007, 19:55
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-table-above-gives-the-number-of-calories-and-grams-of-129998.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Nov 2013, 22:31, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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 [#permalink] New post 16 Mar 2007, 00:04
If we let s be the kgs of S and t be the kgs of T, then the question stem gives you the equation:
s + t = 7

Then we only need another linearly independent equation and we'll be able to solve for both s and t.

Statement (1) tells us 2000s + 1500t = 12000. This is another linearly independent equation, so statment (1) is sufficient.

Statement (2) tells us 150s + 90t = 810, so statement (2) is sufficient as well.

Therefore each statement alone is sufficient. (D)
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 [#permalink] New post 16 Mar 2007, 09:35
I agree and my explanation is same as given. The ans is D
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thanks a bunch [#permalink] New post 16 Mar 2007, 09:35
thanks so much ...for some reason i wd have never thought on these lines !
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Re: Food | Calories per kg | grams of protien per kg S | 2000 | [#permalink] New post 17 Nov 2013, 18:13
Another way of solving this problem. Statement 1: 2000s+ 1500t=12000. Notice that hundreds digit in 12000 is 0. But hundreds digit in 1500 is 5. We need to make it zero. When is it possible? It is possible only when t=2,4 or 6. Corresponding values of s=5,3 or 1(as s+t=7). Take (s,t)=5,2. It does not satisfy the equation. Take (s,t)=3,4. It satisfies. SUFFICIENT . -----------------------------------------------------------------------------------------------------------Statement 2: equation is 150s+90t=810; take s=3 and t=4. Check. satisfies. SUFFICIENT.
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Re: The table above gives the number of calories and grams of pr [#permalink] New post 17 Nov 2013, 22:31
Expert's post
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-table-above-gives-the-number-of-calories-and-grams-of-129998.html
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Re: The table above gives the number of calories and grams of pr   [#permalink] 17 Nov 2013, 22:31
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