karthikpandian19 wrote:Food---Number of Calories per Kilogram---------Number of Grams of Protein per Kilogram
S------------2,000---------------------------------------150
T------------1,500----------------------------------------90

20. The information 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.

s+t = 7
what is the value of s?


(1) The mixture has a total of 12,000 calories.


s+t = 7
2000s + 1500t = 12000
2 eq-- 2 variables
you can find the value of s

Sufficient

(2) The mixture has a total of 810 grams of protein.
150s + 90t = 810
s+t = 7

2eq -- 2 var

Sufficient


Option D

Anurag@Gurome wrote:

karthikpandian19 wrote:Food Number of Calories per Kilogram Number of Grams of Protein per Kilogram
S 2,000 150
T 1,500 90

20. The information 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.

Let x kgs of food S be there in the mixture.
Then T = 7 - x

(1) 2000x + (7 - x)1500 = 12000
10500 + 500x = 12000
500x = 1500 or x = 3; SUFFICIENT

(2) 150x + (7 - x)90 = 810
60x = 180 or x = 3; SUFFICIENT

The correct answer is D.

For solving problems involving mixtures is 'alligation method' the best.
i.e. drawing table and solving . When I try that method for this problem I can easily get the answer of this problem. But to solve it to get correct value of 'x' seems difficult due to fractions involved.
Is there any better method for working with mixtures.

Thanks in advance.

Easier approach to this problem:
S+ T = 7

(1) The mixture has a total of 12,000 calories.
As total calories are 12000 so calories/Kg of T should be a multiple of 12000 - Calories of S
Calories from S could be : 2000 (1Kg), 4000 (2kg), 6000 (3kg), 8000 (4kg), 10000 (5kg), 12000(6kg)
Calories from T could be : 10000 (NAI), 8000 (NAI), 6000 (4kg), 4000 (NAI), 2000 (NAI), 0(0 kg)
Here NAI - not an integer

Total quantity is 7 kg. So from above S = 3kg, T = 4kg. Sufficient

S 2,000 150
T 1,500 90

(2) The mixture has a total of 810 grams of protein.
Here again
Protein from S could be : 150 (1Kg), 300 (2kg), 450 (3kg), 600 (4kg), 750 (5kg)
Protein from T could be : 660 (NAI), 510 (NAI), 360 (4kg), 210 (NAI), 60 (NAI)
Total quantity is 7 kg. So from above S = 3kg, T = 4kg. Sufficient

So Ans : D

I still couldn't able to understand your approach here.

MakeUrTimeCount wrote:Easier approach to this problem:
S+ T = 7

(1) The mixture has a total of 12,000 calories.
As total calories are 12000 so calories/Kg of T should be a multiple of 12000 - Calories of S
Calories from S could be : 2000 (1Kg), 4000 (2kg), 6000 (3kg), 8000 (4kg), 10000 (5kg), 12000(6kg)
Calories from T could be : 10000 (NAI), 8000 (NAI), 6000 (4kg), 4000 (NAI), 2000 (NAI), 0(0 kg)
Here NAI - not an integer

Total quantity is 7 kg. So from above S = 3kg, T = 4kg. Sufficient

S 2,000 150
T 1,500 90

(2) The mixture has a total of 810 grams of protein.
Here again
Protein from S could be : 150 (1Kg), 300 (2kg), 450 (3kg), 600 (4kg), 750 (5kg)
Protein from T could be : 660 (NAI), 510 (NAI), 360 (4kg), 210 (NAI), 60 (NAI)
Total quantity is 7 kg. So from above S = 3kg, T = 4kg. Sufficient

So Ans : D

@Karthik: Let me explain it again:
Total quantity = S + T = 7 kg

1) Total calorie = 12000
If S is 1 Kg (2000 calories), then T should be 7-1 = 6 kg(6*1500 = 9000 calories) => less than 12000 calorie
Likeways,
If S is 2 Kg (4000 calories), then T should be 7-2 = 5 kg (5*1500 = 7500 calories)
If S is 3 Kg (6000 calories), then T should be 7-3 = 4 kg (4*1500 = 6000 calories)
If S is 4 Kg (6000 calories), then T should be 7-4 = 3 kg (3*1500 = 4500 calories)
If S is 5 Kg (6000 calories), then T should be 7-5 = 2 kg (2*1500 = 3000 calories)
If S is 6 Kg (6000 calories), then T should be 7-6 = 1 kg (1*1500 = 1500 calories)

We will get only 1 combination having total of 7 kgs and 12000 calories.

On same lines, we can use data provided in option B)

Hope above make sense...

The answer is D certainly, but guyzzz did you notice one thing...

From statement 1: s = 5 and t = 2

From statement 2: s = 3 and t = 4


Usually this does not happen on the GMAT...

You get the same values from both the statements...

Just check this once...

Thank You...