# ISEE Middle Level Math : Numbers and Operations

## Example Questions

### Example Question #61 : Numbers And Operations

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:

Answer: On average, Natasha can spend \$18.75 per gift.

### Example Question #61 : Numbers And Operations

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 #63 : Numbers And Operations

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 #64 : 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 #65 : Numbers And Operations

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 #66 : Numbers And Operations

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 #67 : 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 #68 : Numbers And Operations

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 #69 : Numbers And Operations

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 #70 : Numbers And Operations

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