# GMAT Math : GMAT Quantitative Reasoning

## Example Questions

### Example Question #13 : Measurement Problems

Fill in the blank:

Explanation:

One yard is equal to 36 inches; one square yard is equal to .

Multiply this conversion factor by 13:

, the correct choice.

### Example Question #21 : Measurement Problems

A jar is 40% full of water. If 250 milliliters of water are added, the jar will be half full. What is the total capacity of the jar?

2 liters

3 liters

2.5 liters

0.5 liters

1.5 liters

2.5 liters

Explanation:

Since the addition of 250 milliliters of water changes the status of the jar from 40% full to half, or 50%, full, then 250 milliliters is  of the capacity of the jar. Therefore, the jar holds

milliliters of water total.

Divide by 1,000 milliliters per liter to convert to liters:

liters.

### Example Question #21 : Measurement Problems

Two jars have identical capacity. The first jar contains 200 milliliters of water. The contents of the second jar, which is 10% full, are poured into the first, after which the first jar contains 250 milliliters.

Give the capacity of the first jar.

0.5 liters

0.25 liters

0.4 liters

1 liter

0.8 liters

0.5 liters

Explanation:

The second jar was 10% full and contained  milliliters of water. Therefore, the capacity of the second jar, which is also that of the first, is

milliliters.

Divide this by the conversion factor of 1,000 to convert to liters:

liters, the correct response.

### Example Question #61 : Problem Solving Questions

Two jars each hold a quantity of water. The first jar is 20% full; the second jar, which has twice the capacity of the first, is 40% full. The total amount of water in the two jars is 600 milliliters.

How much more water will the first (smaller) jar hold before it is completely full?

1.6 liters

0.48 liters

0.72 liters

2 liters

1 liter

0.48 liters

Explanation:

Call the capacity of the first jar, in milliliters, ; the capacity of the second jar is therefore twice this, or

The first jar is 20% full, so the amount of water in this jar is currently  milliliters. The second jar is 40% full, so it contains  milliliters of water. Therefore, since the total amount of water is 600 milliliters:

The first jar has a capacity of 600 milliliters. It is 20% full, so it has

milliliters of water, and it can hold

milliliters more. Divide by 1,000 milliliters per liter to convert to liters:; this is

liters.

### Example Question #61 : Word Problems

Two jars of identical size each hold a quantity of water; the first jar is  full, the second,  full. The total amount of water in the two jars is .

How much more water can be poured into the first jar until it is full?

Explanation:

Since the two jars have the same capacity, which we will call  milliliters, the amount of water in the first and second jars, respectively, are  , and  of , or . The total amount of water is

The capacity of each jar is . The first jar is  full and therefore contains  milliliters of water; it can hold  milliliters more.

Divide by to convert to liters:

.

### Example Question #21 : Understanding Measurement

Two jars each contain a quantity of water. The first jar is filled to capacity. The second jar has 40% greater capacity than the first jar, and contains 20% less water. If the second jar is  full, which of the following is equal to  ?

Explanation:

For the sake of simplicity, assume that the first jar holds 100 milliliters of water - this reasoning is independent of the actual capacity. The second jar holds 40% more water, which is

milliliters capacity.

The first jar is filled to capacity, so it holds 100 milliliters of water. The second jar contains 20% less water, so it contains

milliliters of water.

The jar is  full.

### Example Question #21 : Understanding Measurement

An empty jar has capacity two liters. There are several other jars of equal capacity (to each other, but not necessarily to the first); each contains water to 25% capacity.

The contents of eight of the other jars are emptied into the two-liter jar when it is discovered that there is not enough space left in that jar to hold all of the contents of another of the other jars. What could the capacity of each of the other jars be?

1.3 liters

0.5 liters

0.7 liters

0.9 liters

1.1 liter

0.9 liters

Explanation:

Let  be the capacity, in liters, of each of the other jars. Since each jar is 25% full, the amount of water in each jar is 25% of , or . The contents of eight such jars will fit in the two-liter jar, so

This means each jar can be at most one liter in capacity.

The contents of nine such jars will not fit, however, so

This means that each jar must be at least about 0.88 liters in capacity.

The only choice that falls in this range is 0.9 liters, so this is the correct choice.

### Example Question #63 : Word Problems

A really backward country does not use inches, feet, yards, or meters to measure distance, it uses units called flots, glots, and klots. It takes 17 flots to make a glot, and 7 glots to make a klot.

These units can also be used to form units of area and volume (i.e. square flots, cubic klots).

How many cubic flots make a cubic klot?

Explanation:

First, multiply to find the number of flots in a klot.

Cube that to find the number of cubic flots in a cubic klot.

Therefore, 1,685,159 cubic flots = 1 cubic klot

### Example Question #1 : Calculating Discounts

A refrigorator is on sale for 20% off the original price. A store-wide sale results in an additional reduction of 25%. What is the total discount based on the original price?

60%

45%

55%

40%

40%

Explanation:

Let  equal the original price.

First discount: (sale price).

Second discount: (final sale price)

Therefore, the final price is 60% of the original price. To calculate the discount:

or 40%

### Example Question #1 : Discount

Carolyn won a $450 gift card, and she wants to spend it at the store where she works. Normally, she gets a 10% employee discount, but in one week, her store will be having an "Employee Appreciation Day" during which a 25% employee discount will apply. If, as an employee, she does not have to pay sales tax, how much more worth of merchandise (in terms of price before discount) will she be able to purchase by holding out to that day (nearest cent, if applicable)? Possible Answers: Correct answer: Explanation: Let be the price before discount of the merchandise Carolyn can purchase now using her 10% discount. Then Carolyn will pay 90% of that price, or . Set up and solve the equation: So Carolyn can use that gift card to purchase$500 worth of merchandise now.

Now let  be the price before discount of the merchandise Carolyn can purchase during Employee Appreciation Day using a 25% discount. Then Carolyn will pay 75% of that price, or . Set up and solve the equation:

So Carolyn can use that gift card to purchase $600 worth of merchandise on Employee Appreciation Day. Carolyn can save$100 by holding out.