How to find the whole from the part with percentage - SSAT Middle Level Quantitative

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Question

25% of fish are blue (50 fish). 50% of fish are green (100 fish). The remaining fish are red. How many fish are red?

Answer

First, we need to determine the percentage of fish that are red. So add the percentages of blue and green fish and then subtract this number from 100. So,

and

If you notice that the problem already states how many fish constitute 25 percent, you don’t need to do any more work! Therefore, 50 fish are red.

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Question

Exactly $\frac{1}{3}$ of the plants in a garden are tomato plants. Which of the following could be the total number of plants in the garden?

Answer

The total number of plants has to be divisible by 3. Of the answer choices, the only one that is divisible by 3 is 18. You can check this because numbers that are divisible have the sum of their digits also divisible by 3. For example,

which is divisible by 3, so 18 is divisible by 3.

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Question

0.45 is 24% of what number?

Answer

The answer multiplied by 24%, or, equivalently, 0.24, is 0.45. Subsequently, divide 0.45 by 0.24.

$0.45 \div 0.24 = 1.875$

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Question

of what number is ?

Answer

Taking of a number is the same as multiplying that number by . We can find our number, therefore, by dividing by :

$8,000 \div 0.64 = 12,500$

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Question

330 is 75% of what number?

Answer

330 is 75% of a number we will call ; alternatively, 0.75 multiplied by is equal to 330. Set up this equation and solve for :

$0.75 N \div 0.75 = 330\div 0.75$

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Question

is of what number?

Answer

is of a number we will call ; alternatively, multiplied by is equal to . Set up this equation and solve for :

$0.4 N \div 0.4 = 128\div 0.4$

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Question

32 is $2 \frac{1}{2}$ % of what number?

Answer

We can rewrite $2 \frac{1}{2}$ % as 2.5%. 32 is 2.5% of a number , or, equivalently, 0.025 multiplied by a number is equal to 32. We can write this as an equation and solve for :

$0.025 N \div 0.025 = 32 \div 0.025$

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Question

88 is $12 \frac{1}{2}$ % of what number?

Answer

We can rewrite $12 \frac{1}{2}$ % as 12.5%. 88 is 12.5% of a number , or, equivalently, 0.125 multiplied by a number is equal to 88. We can write this as an equation and solve for :

$0.125 N \div 0.125 = 88 \div 0.125$

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Question

To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 5,319 students, how many signatures must a student get to be on that ballot? (Nearest whole person)

Answer

3% of 5,319 can be calculated by multiplying 5,319 by 0.03, the decimal equivalent of 3%:

$5,319 \times 0.03 = ?$

Multiply 5,319 by 3, then move the decimal point so that two digits are to the right:

$5,319 \times 3 =15,957$ ,

so

$5,319 \times 0.03 = 159.57$

Rounded to the nearest whole number, this is 160 signatures.

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Question

Refer to the above diagram. If there were voters who were registered as neither Republicans nor Democrats in Smith County in , how many voters (nearest whole number) were there total?

Answer

of the voters were unaffiliated, and were affiliated with other parties, so of the voters were registered as neither Republicans nor Democrats. Since of the voters numbered , we can find the total number of voters by setting up and solving a proportion:

$\frac{42}{100} = \frac{4,934}{N}$

$42 N = 100 \cdot 4,934$

$42 N \div 42 = 493,400 \div 42$

which rounds to voters.

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Question

3,200 is 160% of what number?

Answer

Set up the proportion statement and solve for by cross-multiplying:

$\frac{3,200}{N}= \frac{160}{100}$

$N \cdot 160 = 3,200 \cdot 100 = 320,000$

$N \cdot 160 \div 160 = 320,000\div 160$

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Question

12 is $\frac{3}{4} %$ of what number?

Answer

Set up the proportion statement and solve for by cross-multiplying:

$\frac{12}{N } = \frac{\frac{3}{4}}{100}$

$\frac{3}{4} \cdot N = 12 \cdot 100 = 1,200$

$\frac{4}{3} \cdot \frac{3}{4} \cdot N = \frac{4}{3} \cdot 1,200$

$N = \frac{4,800}{3} =1,600$

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Question

If 40 percent of a number is 44, what is 60 percent of the same number?

Answer

To determine what 60 percent of the number is, one must first determine what the number is. To find the number, set up a proportion relating the original percentage and the value of the percentage where the top number is the fractional value and the bottom number is the total.

$\frac{Portion}{Total}=\frac{40 percent}{100 percent}=\frac{44}{number}$

Use cross multiplication to solve for the number.

Once the number is found, the new percentage can be found. There are two ways to do this: multiplication or a proportion.

Multiplication:

Proportion: $\frac{60percent}{100percent}=\frac{x}{110}$

This means that 60 percent of the number is 66.

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Question

25% of fish are blue (50 fish). 50% of fish are green (100 fish). The remaining fish are red. How many fish are red?

Answer

First, we need to determine the percentage of fish that are red. So add the percentages of blue and green fish and then subtract this number from 100. So,

and

If you notice that the problem already states how many fish constitute 25 percent, you don’t need to do any more work! Therefore, 50 fish are red.

Compare your answer with the correct one above

Question

Exactly $\frac{1}{3}$ of the plants in a garden are tomato plants. Which of the following could be the total number of plants in the garden?

Answer

The total number of plants has to be divisible by 3. Of the answer choices, the only one that is divisible by 3 is 18. You can check this because numbers that are divisible have the sum of their digits also divisible by 3. For example,

which is divisible by 3, so 18 is divisible by 3.

Compare your answer with the correct one above

Question

0.45 is 24% of what number?

Answer

The answer multiplied by 24%, or, equivalently, 0.24, is 0.45. Subsequently, divide 0.45 by 0.24.

$0.45 \div 0.24 = 1.875$

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Question

of what number is ?

Answer

Taking of a number is the same as multiplying that number by . We can find our number, therefore, by dividing by :

$8,000 \div 0.64 = 12,500$

Compare your answer with the correct one above

Question

330 is 75% of what number?

Answer

330 is 75% of a number we will call ; alternatively, 0.75 multiplied by is equal to 330. Set up this equation and solve for :

$0.75 N \div 0.75 = 330\div 0.75$

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Question

is of what number?

Answer

is of a number we will call ; alternatively, multiplied by is equal to . Set up this equation and solve for :

$0.4 N \div 0.4 = 128\div 0.4$

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Question

32 is $2 \frac{1}{2}$ % of what number?

Answer

We can rewrite $2 \frac{1}{2}$ % as 2.5%. 32 is 2.5% of a number , or, equivalently, 0.025 multiplied by a number is equal to 32. We can write this as an equation and solve for :

$0.025 N \div 0.025 = 32 \div 0.025$

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