ISEE Lower Level Math : Whole and Part

Study concepts, example questions & explanations for ISEE Lower Level Math

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Example Questions

Example Question #11 : Whole And Part

There are 4 canoes at a summer camp. Each canoe can hold a maximum of 6 campers, but each canoe must have an even number of campers in order to maintain balance.

Which of the following is NOT a possible number of campers who could have paddled from one end of the lake to the other using all 4 canoes?

Possible Answers:

Correct answer:

Explanation:

If each canoe requires an even number of campers, then it would have been impossible for 6 campers to have paddled across in all 4 canoes.

This is because if 6 campers used the canoes, 2 campers would have gone the first two canoes, while 1 camper would have gone in each of the 2 remaining canoes. Only having 1 camper per canoe would have been an odd number of campers, causing the canoe to be unbalanced.

6 campers:

Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 1, Canoe 4 - 1

In order for each canoe to have an even number of campers, there must be a minimum of 8 campers.

If there were 8 campers:

Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 2, Canoe 4 - 2

If there were 12 campers:

Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 2, Canoe 4 - 6

If there were 14 campers:

Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 4, Canoe 4 - 6

If there were 20 campers:

Canoe 1 - 4, Canoe 2 - 4, Canoe 3 - 6, Canoe 4 - 6

Example Question #12 : Whole And Part

Greg eats 4 brownies, which is equal to  of the total batch. How many brownies are in the total batch?

Possible Answers:

Correct answer:

Explanation:

If b is equal to the number of brownies in the batch, the following equation can be used to determine the value of b:

Given that 4 is twice the value of 2, it follows that b will be twice the value of 17. Therefore, the value of b is 17 mutliplied by 2, which is 34. 

Example Question #13 : Whole And Part

There are four tea bags left in a box. If this quantity is 25% of the original, how many tea bags were originally in the box?

Possible Answers:

Correct answer:

Explanation:

We can set up a proportion to solve:

Cross-multiply:

Example Question #14 : Whole And Part

What is the value of the expression below?

Possible Answers:

Correct answer:

Explanation:

To solve the expression, , the key is to reduce it step by step, as shown below:

Example Question #15 : Whole And Part

What is the value of the expression below?

Possible Answers:

Correct answer:

Explanation:

To solve , the expression must be reduced step by step, starting with the parentheses. 

Negative 7 and positive 7 cancel each other out. 

Therefore, 1 is the correct answer. 

Example Question #16 : Whole And Part

If there are 4 servings in an ice cream container, and each serving is equal to 2 ounces, how many ounces are in the entire container?

Possible Answers:

Correct answer:

Explanation:

If an ice cream container has 4 servings and each serving is equal to 2 ounces, the total number of ounces in the container can be found by multiplying 2 by 4.

This results in 8 ounces. 

Example Question #17 : Whole And Part

If one-third of a pie is equal to 2 slices, how many slices are in the entire pie?

Possible Answers:

Correct answer:

Explanation:

We know that one-third of the pie is 2 slices. We can set up an equation:

In other words, one-third times the total slices in the pie will be equal to 2 slices.

Multiply both sides of the equation by 3.

The fraction on the left side cancels.

There are a total of 6 slices in the pie.

Example Question #18 : Whole And Part

If Gina makes a batch of cookies for her class. The class eats  of the cookies, and so  remain. How many cookies were in the entire batch?

Possible Answers:

Correct answer:

Explanation:

If the class eats  of the cookies and  remain, this means that . Therefore,  of the batch will be equal to  cookies, as  is twice the value of , and  is twice the value of

The entire batch of cookies will be equal to .

Thus,  is the correct answer. 

Example Question #19 : Whole And Part

If Andrew has coins in his wallet that add up to  cents, which of the following is a possible combination of coins that he may have?

Possible Answers:

 quarter,  dimes,  nickels, and  pennies

 quarter,  dimes,  nickels, and  pennies

 quarters,  dimes,  nickels, and  pennies

 quarter,  dimes,  nickels, and  penny

Correct answer:

 quarter,  dimes,  nickels, and  pennies

Explanation:

The first step is to convert the coins into their values in cents. 

If we look at the combination of  quarter,  dimes,  nickels, and  pennies, the following expression can be used to determine the coins' value in cents:

Therefore, the correct answer is  quarter,  dimes,  nickels, and  pennies.

As for the incorrect answers,  quarter,  dimes,  nickels, and  penny adds up to  cents;  quarters,  dimes,  nickels, and  pennies adds up to  cents; and  quarter,  dimes,  nickels, and  pennies adds up to  cents.

Example Question #20 : Whole And Part

If Lisa buys a pair of shoes for , but the sales tax is , what is the total cost of her shoes in dollars?

Possible Answers:

Correct answer:

Explanation:

If the sales tax is , then this means that for every purchase of , an  tax will be charged. 

Given that the shoes are  (half of ), half the sales tax of  should be charged, which is a value of

Since , the shoes will cost  after sales tax. 

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