### All SAT Math Resources

## Example Questions

### Example Question #2031 : Psat Mathematics

If of is , then what is of ?

**Possible Answers:**

50

10

20

200

100

**Correct answer:**

50

The first part of the problem tells us that x% of 20 is 50. We can model x% as x/100 or 0.01x. To find x% of 20, we can multiply 0.01x and 20. In other words, we can write the following equation:

(0.01x)(20) = 50

Divide both sides by 20.

0.01x = 2.5

Divide both sides by 0.01.

x = 250.

The question then asks us to find 20% of x. We can represent 20% as 0.2, and we know that x is 250. Therefore,

20% of 250 = 0.2(250) = 50.

The answer is 50.

### Example Question #2032 : Psat Mathematics

If of a number is , what is of the number?

**Possible Answers:**

**Correct answer:**

Let x be the number in question.

Then 2/3 * x = 18.

x = 18 * 3/2 = 27

Now find 1/9 of 27:

1/9 * 27 = 3

### Example Question #41 : Percentage

17 is 85% of what number?

**Possible Answers:**

**Correct answer:**

In this case, 17 is part of a whole x. We are also given that 17 is 85% of x.

With this in mind, we can set up the following proportion.

To solve for x, cross multiply.

### Example Question #6 : How To Find The Whole From The Part With Percentage

On the ride home from school, Jim notices that pecent of the cars he passes are yellow. Jim sees yellow cars. How many cars does Jim see that aren't yellow?

**Possible Answers:**

**Correct answer:**

Let x represent the total number of cars Jim sees on the way home. If Jim sees 7 yellow cars and notices that 35% of all the cars he sees are yellow, then we can express this as

7/x = 35%, or

Using cross multiplication, we see that

Therefore, Jim sees 20 total cars on the way home. The question wants to know how many cars are NOT yellow. We can find that by subtracting the total number of cars from the number of yellow cars:

### Example Question #7 : How To Find The Whole From The Part With Percentage

is of what number?

**Possible Answers:**

None of the given answers are correct.

**Correct answer:**

To solve this problem, we can set up a proportion and solve for our missing value using cross multiplication.

### Example Question #41 : Percentage

is of what number?

**Possible Answers:**

**Correct answer:**

Don't let the pi throw you off on this question. We can set up a proportion to solve for the whole that we are looking for.

(Remember that any percentage can also be written as a fraction.)

Now we can solve for our unknown by using cross multiplication.

Therefore, is of .

### Example Question #42 : Percentage

is of what number?

**Possible Answers:**

**Correct answer:**

We can set up a proportion to solve this problem. Remember that we can express percentages as fractions.

Now we can cross-multiply and solve for our unknown.

### Example Question #42 : Percentage

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

**Possible Answers:**

2

49

11

155

13

**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 #43 : Percentage

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:**

–3/2

–2/3

3/2

2/3

–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 #61 : Percentage

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

**Possible Answers:**

125

133

25

75

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.

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