GMAT Math : Mixture Problems

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #21 : Mixture Problems

Before being slightly dried, an apple is made of  of water. After the apple is slightly dried, the water accounts only for  of the weight of the fruit. Originally, the apple weighed . What is its weight after being dried? Consider the difference in weight to be solely caused by the evaporating water.

Possible Answers:

Correct answer:

Explanation:

First, we should find out what isn't water in the apple; let's call this the pulp. The pulp accounts for  of the weight of the fruit before being dried. Therefore, the pulp weighs . We can then express as a ratio the amount of pulp in the apple to the total weight of the fruit after it has been slightly dried as follows: 

We can rearrange this equation to yield: 

The weight of the water in the dried fruit is therefore . To this weight we simply add the weight of the pulp and we get the final answer, 

Example Question #181 : Gmat Quantitative Reasoning

Two jars of equal size each contain some saltwater solution. The first jar is 20% full of a solution which is 80% salt; the second jar is 80% full of a solution which is 20% salt. The contents of the jars are mixed. What is the concentration of salt in the combined solution?

Possible Answers:

Correct answer:

Explanation:

For the sake of simplicity, assume that each jar holds 100 milliliters of water - this reasoning is independent of the actual capacity. 

The first jar is 20% full, so it contains  milliliters of solution; this solution is 80% salt, so there are  millilters of salt in the solution. Similarly, the second jar includes  milliliters of solution, which include  milliliters of salt.

Therefore, when the two solutions are mixed, the concentration of salt will be

.

Example Question #181 : Word Problems

Two jars of equal capacity each contain a saltwater solution. The first jar is 40% full, and its solution is 60% salt. If the contents of the second jar are emptied into the first jar, the solution, which will fill the jar completely, will be 30% salt. 

What is the salt concentration of the contents of the second jar?

Possible Answers:

Correct answer:

Explanation:

For the sake of simplicity, let us assume that each jar has capacity 100 milliliters; the reasoning is the same regardless of the common capacity. 

The first jar is 40% full, so there are  milliliters of solution in the jar; the solution is 60% salt, so there are  milliliters of salt in the solution. 

For the first jar to be filled to capacity,  milliliters of solution must be added. Also, if the solution is 30% salt, then the jar will contain milliliters of salt. This means that  milliliters of salt will have been added. This means that the concentration of salt in the added solution - the contents of the second jar - is

.

(Note that the actual size of the second jar does not matter.)

 

Example Question #181 : Problem Solving Questions

Charlie, the barrista at Sunday Coffee, has a problem. He must mix together Licorice Dream tea, which costs $20/lb, and Strawberry Explosion tea, which costs $12/lb to make sixty pounds of a new flavor of tea. Unfortunately, he forgot the correct proportions. He does know that the new tea costs $14/lb.

How many pounds of the Licorice Dream tea go into the mix? 

(You may assume that the tea is to sell for the same amount of money as if it had been sold separately.)

Possible Answers:

None of the other answers are correct

Correct answer:

None of the other answers are correct

Explanation:

Let  be the number of pounds of Licorice Dream tea; then  is the number of pounds of Strawberry Explosion. Then the total value of each ingredient tea, as well as the total value of the new tea, will be:

Licorice:  or 

Strawberry:  or 

New tea: 

 

Add the individual costs of the ingredient teas to get the total cost of the new tea.

Charlie will use 15 pounds of the Licorice Dream; as this is not one of the given answers, the correct answer is "None of the answers are correct".

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