A juice bar mixed apple juice and berry concentrate to make 6 liters

Question

A juice bar mixed apple juice and berry concentrate to make 6 liters of a fruit drink. If apple juice cost $4 per liter, and berry concentrate cost $10 per liter, was the volume of apple juice used greater than the volume of berry concentrate used?

(1) Less than 4 liters of berry concentrate were used.

(2) The total cost of the apple juice and berry concentrate used to make the 6 liters of fruit drink was less than $39.

M47-174

Bunuel · Accepted Answer

GMAT Club Official Solution:

A juice bar mixed apple juice and berry concentrate to make 6 liters of a fruit drink. If apple juice cost $4 per liter, and berry concentrate cost $10 per liter, was the volume of apple juice used greater than the volume of berry concentrate used?

Let x be the number of liters of berry concentrate used. Since the fruit drink was 6 liters total, the amount of apple juice used was 6 - x. The question asks:

Is 6 - x > x?

Is x < 3?

So the question is equivalent to asking whether less than 3 liters of berry concentrate were used.

(1) Less than 4 liters of berry concentrate were used.

This tells us:

x < 4

This is not enough.

Not sufficient.

(2) The total cost of the apple juice and berry concentrate used to make the 6 liters of fruit drink was less than $39.

The apple juice cost $4 per liter, and the berry concentrate cost $10 per liter, so:

4(6 - x) + 10x < 39

24 - 4x + 10x < 39

x < 2.5

Since x < 2.5, we know x < 3. Therefore, more apple juice than berry concentrate was used.

Sufficient.

Answer: B.

Amity007 · Answer

Correct answer seems to be B.
Here we need to figure out if apple juice quantity > Berry quantity?

Statement 1: berry used less than 4 litre, that can be 3.5 or 2.5 or 3 as well. By this alone we cant be sure about quantities.

Statement 2: the combined cost is < 39. Here we would be make following 2 categories.
1. when berries is greater than apple --> if 4 ltr of berries and 2 ltr of apple juice is used the total cost would be 4x10 + 2x4 which i greater than 39
2. Lets assume both are in equal quantity--> so 3ltr x 10(for berries) + 3ltr x 4(for apple juice) this will also be 42 which is greater than 39.

Now from 2nd statement we are sure that quantity of berries is definitely less than apple juice. So B is sufficient.

ariyanak · Answer

(1) is clearly not sufficient because less than 4 liters of berry concentrate could mean 3 and 3 but also 3.9 (B) and 2.1 (A) and 2.9 (B) and 3.1 (A).

(2) we can derive that the average cost is less than $6.5 / liter. Which is closer to the per liter cost of apple concentrate ($4) vs berry concentrate ($10). Hence, this tells me the apple concentrate more dominant in the mixture.

Hence (B).

A juice bar mixed apple juice and berry concentrate to make 6 liters

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GMAT Data Sufficiency (DS) Questions

A juice bar mixed apple juice and berry concentrate to make 6 liters

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