### All ISEE Middle Level Math Resources

## Example Questions

### Example Question #28 : How To Find The Part From The Whole

There are 15 animals in a pet store. The only animals are dogs and cats. There are twice as many dogs as cats. How many dogs are there?

**Possible Answers:**

**Correct answer:**

In this problem, the sum of the cats and dogs must equal 15. If there are 10 dogs, there must be 5 cats because there are twice as many dogs as cats. (Two times 5 is 10.)

Given that 10 plus 5 is 15, 10 is the correct answer.

### Example Question #21 : How To Find The Part From The Whole

A dog has a litter of 6 puppies. The average weight of the puppies is 7 pounds. After one week, half of the puppies have gained one pound. What is the new average weight of the puppies after one week?

**Possible Answers:**

**Correct answer:**

If half of the 6 puppies gain one pound, that means that 3 puppies will gain one pound. This means that 3 total pounds will be gained among the 6 puppies.

We can assume that the weight of each puppy was originally 7 pounds, since the average was 7. Three of the puppies have gained a pound, meaning they will weigh 8 pounds.

Weights of the puppies after one week: 7, 7, 7, 8, 8, 8

Find the new average by summing the individual weights and dividing by the number of puppies.

### Example Question #22 : How To Find The Part From The Whole

Brett buys a shirt. The original price was , but the shirt is on sale for off. Additionally, Brett has a off coupon that he uses after the off is applied. What is the price of the shirt in dollars, before tax?

**Possible Answers:**

**Correct answer:**

If the original price of the shirt was , but it is on sale for off, then that means the shirt will be discounted by because of is . . Additionally, with the off coupon, the final price would be .

### Example Question #23 : How To Find The Part From The Whole

Sweaters are each, but they are on sale: when you buy one, you get one free. Rebecca buys one sweater and gets one free. At checkout, she then presents a coupon for an additional off. What is the average cost of one sweater in dollars (before tax)?

**Possible Answers:**

**Correct answer:**

If Rebecca buys a sweater that is part of a buy one, get one free sale, that means that she will get two sweaters for a total of . A off discount will mean that Rebecca will save off of her total because of is .

Therefore, the total she will pay is equal to .

The average price of a sweater will therefore be .

### Example Question #22 : How To Find The Part From The Whole

of the students in a classroom of students are boys. of the girls in this classroom wear their hair in pigtails. How many girls wear their hair in pigtails?

**Possible Answers:**

**Correct answer:**

If of the students in a classroom of students are boys, that means that students are boys, since . (Alternatively, you could figure this out by realizing that since of is and , of must equal , which is .) If there are boys in the classroom, there must be girls, since .

Given that of the girls wear their hair in pigtails, and of is , it follows that there are girls in the classroom who wear their hair in pigtails.

### Example Question #61 : Numbers And Operations

If the sum of 3 consecutive numbers is 111, what is the value of the middle number?

**Possible Answers:**

**Correct answer:**

The sum of . The easiest way to discover the middle number of this set is to divide 111 by 3:

Now that you have the middle number, simply add one to it and subtracy one from it to get your consecutive numbers:

### Example Question #24 : How To Find The Part From The Whole

3 brothers weigh 80 pounds, 120 pounds, and 135 pounds. The smallest brother gained 15 pounds over the past year, while the largest brother lost 5 pounds. The middle brother's weight did not change. Based on the brothers' new weights, what is their average weight?

**Possible Answers:**

**Correct answer:**

If 3 brothers weigh 80 pounds, 120 pounds and 135 pounds, and the smallest brother gained 15 pounds over the past year, while the largest brother lost 5 pounds, the new weights of the brothers are:

95 pounds, 120 pounds, and 130 pounds. (The middle brother's weight did not change.)

Given that the average is found by dividing the sum of the numbers in a list by the number of items in that list, the following equation will be used:

Therefore, the new average is 115 pounds.

### Example Question #25 : How To Find The Part From The Whole

If 25 percent of a number is 3, then what would two thirds of the same number be equal to?

**Possible Answers:**

**Correct answer:**

If 25 percent of a number is 3, then that means that 100 percent of the number will be equal to 3 times 4, which is 12. Two thirds of the number 12 is 8; therefore, 8 is the correct answer.

### Example Question #26 : How To Find The Part From The Whole

Stephanie needs to drive miles to meet her family at their vacation home. If she drives at miles per hour, how many hours will it take Stephanie to arrive?

**Possible Answers:**

**Correct answer:**

Divide:

Answer: It will take Stephanie hours to arrive.

### Example Question #21 : How To Find The Part From The Whole

Eighteen dollars must be shared among friends. How much money will each friend receive?

**Possible Answers:**

**Correct answer:**

Divide:

Answer: Each friend will receive .