### All SAT Math Resources

## Example Questions

### Example Question #1 : Decimals And Percentage

55 and 1/2% of 23 is about what?

**Possible Answers:**

2

13

155

11

49

**Correct answer:**

13

55 and 1/2% can be written as a decimal: 0.555. To see what number is about 55.5% of 23, multiply 0.555 by 23. Answer: 12.765 or about 13.

Another route is to say that 55.5% is about half of 23. Half of 23 is 11.5. Since 55.5% is greater than 50%, 13 is the logical choice instead of 11.

### Example Question #211 : Arithmetic

Let *x* and *y* be numbers such that *x* and *y* are both nonzero, and *x* > *y*. If half of *x* is equal to thirty percent of the positive difference between *x* and *y*, then what is the ratio of *x* to *y*?

**Possible Answers:**

2/3

–3/2

–2/3

3/2

–1

**Correct answer:**

–3/2

We need to find expressions for fifty percent of *x* and for thirty percent of the positive difference between *x* and *y*. Then, we can set these two expressions equal to each other and determine the ratio of *x* to *y*.

Fifty percent of *x* is equal to one-half of *x*, which is the same as multiplying *x* by 0.50.

50% of *x* = 0.5*x*

Thirty percent of the positive difference between *x* and *y* means that we need to multiply the positive difference between *x* and *y* by thirty percent. Because *x* > *y*, the positive difference between *x* and *y* is equal to *x* – *y*. We then need to take thirty percent of the quantity *x* – *y*. Remember that to convert from a percent to a decimal, we move the decimal two spaces to the left. Therefore, 30% = 0.30. We can now multiply this by (*x –* *y*).

30% of *x* – *y* = 0.30(*x* – *y*)

Now, we set the two expressions equal to one another.

0.5*x* = 0.30(*x* – *y*)

Distribute the right side.

0.5*x* = 0.3*x* – 0.3*y*

The ratio of *x* to *y* is represent by *x*/*y*. Thus, we want to group the *x* and *y* terms on opposite sides of the equations, and then divide both sides by *y*.

0.5*x* = 0.3*x* – 0.3*y*

Subtract 0.3*x* from both sides.

0.2*x* = –0.3*y*

Divide both sides by 0.2

*x* = (–0.3/0.2)*y*

Divide both sides by *y* to find *x*/*y*.

*x*/*y* = (–0.3/0.2) = –1.5.

Because the answers are in fractions, we want to rewrite –1.5 as a fraction. We can write –1.5 as –1.5/1 and then mutiply the top and bottom by 2.

(–1.5/1)(2/2) = –3/2

The answer is –3/2

### Example Question #212 : Arithmetic

If of is equal to of , and of is equal to of , then what percent of is ?

**Possible Answers:**

133

75

125

25

100

**Correct answer:**

75

We are told that 50% of *x* is equal to 25% of *y*. We need to represent these two pieces of information as algebraic expressions. We can convert 50% and 25% to decimals by moving the decimals two places to the left. Thus, 50% = 0.50, and 25% = 0.25. To find 50% of *x*, we multiply *x* by 0.50. In other words, 50% of *x* = 0.50*x*. Likewise, 25% of *y* = 0.25*y*. We now set 0.50*x* and 0.25*y* equal to one another.

0.50*x* = 0.25*y*

Let's divide both sides by 0.25 to get rid of decimals.

2*x* = *y*

Next, we are told that 40% of *y* is equal to 60% of *z*. We will represent 40% and 60% as 0.40 and 0.60, respectively. Thus, we can write the following equation:

0.40*y* = 0.60*z*

Ultimately, we are asked to find *x* as a percentage of *z*. This means we want to find an equation with *x* and *z*, but not *y*. If we solve for *y* in the second equation, and then substitute this value into the first, we can eliminate *y*.

Let's take the equation 0.40*y* = 0.60*z* and divide both sides by 0.40.

*y* = 1.5*z*

Now, we can take 1.5*z* and substitute this for *y* in the first equation.

2*x* = 1.5*z*

In order to find *x* as a percent of *z*, we must solve for *x* in terms of *z*. This means we must divide both sides of the equation by 2.

*x* = 0.75*z*

*x* is 0.75 times *z*. We can represent 0.75 as 75%, because in order to convert from a decimal to a percent, we need to move the decimal two spaces to the right. Therefore, if *x* = 0.75*z*, then *x* = 75% of *z*.

The answer is 75.

### Example Question #4 : How To Find Decimal Equivalent To A Percentage

What is in decimal form?

**Possible Answers:**

**Correct answer:**

The correct answer is .

This can be obtained by taking the percentage of and dividing by .

This shifts the decimal place over two places to the left, which results in as the decimal of .

### Example Question #5 : How To Find Decimal Equivalent To A Percentage

Find the decimal equivalent to the percentage:

**Possible Answers:**

**Correct answer:**

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

### Example Question #6 : How To Find Decimal Equivalent To A Percentage

Find the decimal equivalent to the percentage:

**Possible Answers:**

**Correct answer:**

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

### Example Question #7 : How To Find Decimal Equivalent To A Percentage

Find the decimal equivalent to the percentage:

**Possible Answers:**

**Correct answer:**

In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

### Example Question #8 : How To Find Decimal Equivalent To A Percentage

Find the decimal equivalent to the percentage:

**Possible Answers:**

**Correct answer:**

### Example Question #9 : How To Find Decimal Equivalent To A Percentage

Find the decimal equivalent to the percentage:

**Possible Answers:**

**Correct answer:**

### Example Question #10 : How To Find Decimal Equivalent To A Percentage

Find the decimal equivalent of the percentage:

**Possible Answers:**

**Correct answer:**

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