# ISEE Middle Level Math : Numbers and Operations

## Example Questions

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

Natasha is going Christmas shopping for the twelve people on her list. On average, how much money can she spend per gift if she has a $225.00 budget? Possible Answers: Correct answer: Explanation: Divide$225 by 12:

### Example Question #27 : How To Find The Part From The Whole

Which of the following is a factor of 72?

None of these

Explanation:

Factors can be multiplied to get a certain number; when a certain number is divided by a factor, the result is a whole number.

When 18 and 4 are multiplied, the result is 72; thus, 18 and 4 are both factors of 72.

When 72 is divided by the other answer choices, a whole number does NOT result.

### 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?

Explanation:

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 #61 : Numbers And Operations

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?

Explanation:

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 #21 : 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?

Explanation:

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 #31 : 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)?

Explanation:

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 #61 : Numbers And Operations

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?

Explanation:

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 #32 : How To Find The Part From The Whole

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

Explanation:

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?

Explanation:

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 #62 : Numbers And Operations

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