How to find the part from the whole

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ISEE Middle Level Quantitative Reasoning › How to find the part from the whole

Questions 1 - 10

In March, there were 10 sunny days, 10 cloudy days, and 11 rainy days. How many days did it rain in March?

Explanation

Identify the number of rainy days in March: days

Katie collects trading cards. 15% of her collection are rare cards. If there are a total of 500 cards in Katie's collection, how many of them are rare?

Explanation

To begin, you can set up a proportion:

$\frac{15}{100}=\frac{x}{500}$

When trying to find a percent of a number, convert the percent into a decimal. To do this, divide the percent by 100.

$15 \div 100 = 0.15$

$0.15=\frac{x}{500}$

You then multiply 500 by 0.15. Since 500 represents 100% of Katie's cards, multiplying by 0.15 will give you how many cards equal 15% of the total.

$x=500 \times 0.15 = 75$

The result is your answer.

Which of the following numbers yields a remainder of 7 when divided by 9?

Explanation

We can test each of the numbers in tun by dividing each by 9:

$104 \div 9 = 11 \textrm{ R }5$

$106 \div 9 = 11 \textrm{ R }7$

$108 \div 9 = 12\textrm{ R }0$

$110 \div 9 = 12 \textrm{ R }2$

106 is the correct choice.

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.

Seventy people need to make five equal lines. How many people will be on each line?

Explanation

Divide:

$70\div 5=14$ people per line

Amir will be selling 20% of his stamp collection. If he has 60 stamps now, how many will he have after he sells some of his stamps?

Explanation

If Amir gets rid of 20% of his cards, he will only have 80% of his cards remaining afterwards.

Therefore, we can figure out how many cards Amir will have after selling 20% of his cards by multiplying times 80% since that will be the amount of cards he will have left, compared to the original number.

To do this, first divide the percentage by 100.

$80 \div100 = 0.8$

Then, multiply the result of this times 60.

$60 \times 0.8 = 48$

The result is your answer.

You and you friends make doing some yard work. If you have four friends and you need to split the revenue evenly, how much do you make?

Explanation

Since there are five of people to split it (you and four friends) you must divide the by which is,

$\frac{$25}{5}=\frac{5\cdot $5}{5}=$5$ .

Julie gets paid $304 a week for dogsitting. If she wants to buy a new washing machine that costs $1400, how many weeks does Julie need to work to save up the required amount? Round to the nearest whole week.

Explanation

Divide the cost of the washing machine by the amount of money she makes each week:

$1400\div 304=4.6$

Answer: Julie needs to save for 5 weeks.

Amanda has 3 more marbles than Jason and 5 fewer marbles than Kate. Together, they all have 17 marbles. How many marbles does Amanda have?

5 marbles

4 marbles

6 marbles

7 marbles

Explanation

Amanda has 3 more marbles than Jason and 5 fewer marbles than Kate. Together, they all have 17 marbles.

To solve this problem, we should experiment by picking a number for Amanda. We can pick the number 4.

If Amanda has 4 marbles, this means that Jason has 1 marble, since Amanda has 3 more. If she has 5 fewer marbles than Kate, that means that Kate must have 9 marbles.

This leaves us with:

Amanda - 4 marbles

Jason - 1 marble

Kate - 9 marbles

This adds up to a total of 14 marbles. However, we know that there are a total of 17 marbles. Thus, each child must have 1 more marble than what is stated above. The correct information would be below:

Amanda - 5 marbles

Jason - 2 marble

Kate - 10 marbles

Here, the sum of the marbles is 17 and Amanda still has 3 more marbles that Jason and 5 fewer marbles that Kate.

Thus, the correct answer is that Amanda has 5 marbles.

What is 60% of 120?