A beverage company prepared two batches of sports drink, Batch A and B

Question

A beverage company prepared two batches of sports drink, Batch A and Batch B, by mixing electrolyte concentrate with water. Batch A contained 25% electrolyte concentrate by volume, and Batch B contained 40% electrolyte concentrate by volume. What was the volume of Batch A?

(1) The total volume of electrolyte concentrate in the two batches was 34 liters.
(2) The total volume of the two batches was 100 liters.

ankushsambare · Answer

Let volume of Batch A = x liters
Let volume of Batch B = y liters
Batch A has 25% electrolyte concentrate → 0.25x
Batch B has 40% electrolyte concentrate → 0.40y
We are given total concentrate = 34
So:
0.25x + 0.40y = 34
We need to find x.
Statement (1)
0.25x + 0.40y = 34
One equation with two variables, so x cannot be uniquely determined.
Not sufficient.
Statement (2)
x + y = 100
One equation with two variables, so x cannot be uniquely determined.
Not sufficient.
Combine (1) and (2)
x + y = 100 → y = 100 − x
Substitute into the first equation:
0.25x + 0.40(100 − x) = 34
0.25x + 40 − 0.40x = 34
−0.15x + 40 = 34
−0.15x = −6
x = 40
Unique value obtained.
Both statements together are sufficient.
 Answer: C

suntprovident · Answer

Let us try to solve the question logically -

Step 1 - Identify the question -

We are given 2 Drinks which are combined to form a 3rd Mixture. Problem pertains to Mixture.

Step 2 - Plan

Ok so we have to 2 Mixtures

A has 25% Electrolytes, B has 40% electrolytes so 2 variables.

Statement 1 tells us that total electrolyte is 34 ltrs

So 0.25x + 0.40y = 34

There can be numerous equations hence this is not sufficient

Statement II similarly gives us that total quantity is 100 which will also give us many equations. Hence not sufficient.

Combining both, we can get 1 unique set of answers. Hence both statements would be required to arrive at a unique value.

BongBideshini · Answer

Let:
 
 Volume of Batch A = A liters 
 Volume of Batch B = B liters

Statement (1): 
The total volume of electrolyte concentrate in the two batches was 34 liters.
This gives:
0.25A + 0.40B = 34

Sometimes one equation can still be sufficient if it leads to only one possible value of the required variable.
Will check whether we can get more than one value.

Try A = 40:
0.25(40) + 0.40B = 34
10 + 0.40B = 34
0.40B = 24
B = 60

Try A = 80:
0.25(80) + 0.40B = 34
20 + 0.40B = 34
0.40B = 14
B = 35

Statement (1) is NOT sufficient.

Statement (2): 
A + B = 100
 Statement (2) alone is also NOT sufficient .

Combining Statements (1) and (2): 
We have two different equations, so we can easily find A. 
 Both statements together are sufficient 
 
Answer: C

A beverage company prepared two batches of sports drink, Batch A and B

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GMAT Data Sufficiency (DS) Questions

A beverage company prepared two batches of sports drink, Batch A and B

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