### All PSAT Math Resources

## Example Questions

### Example Question #11 : How To Evaluate Algebraic Expressions

Drink A is 20% water by weight, and drink B is 35% water by weight. How many fluid ounces of drink A must be added to 80 oz of drink B to have a drink whose final proportion of water is 30%?

**Possible Answers:**

50 fl oz

75 fl oz

40 fl oz

85 fl oz

60 fl oz

**Correct answer:**

40 fl oz

It's easiest if we convert all percentages to actual oz of water for each step here. As such, 35% of the 80 oz of drink B would have 0.35(80) = 28 oz of water in it.

We can set up an equation that similarly converts each "percentage of a fixed weight of liquid" to ensure that our final weight is equivalent to 30% to the sum of drink A and B. On the left side, the fixed values are the percentages of each drink individually, and on the right side is what the question *requires *as a fixed percentage of the final weight:

0.2(A) + 0.35(80) = 0.3(A + 80)

0.2A + 28 = 0.3A + 24

**A = 40 **

Solving for A, we get 40 oz of A that must be poured into B. You may plug this back into the equation to check it.

### Example Question #11 : Evaluating Expressions

Let x&y = xy – x + y. Which of the following is equal to 5&3 ?

**Possible Answers:**

3&(5&2)

4&(3&4)

8&(2&0)

2&(8&1)

11&(0&2)

**Correct answer:**

11&(0&2)

First, we need to evaluate 5&3.

Since x&y = xy – x + y, we can find 5&3 as follows:

5&3 = 5(3) – 5 + 3

= 15 – 5 + 3

= 13

Now, we need to go through each of the choices and determine which one equals 13.

Let's start with 2&(8&1). Remember that we must first evaluate inside the parantheses.

2&(8&1) = 2&(8(1) – 8 + 1)

= 2&(8 – 8 + 1)

= 2&(1)

= 2(1) – 2 + 1 = 1, which doesn't equal 13.

Next, let's evaluate 4&(3&4).

4&(3&4) = 4&(3(4) – 3 + 4)

= 4&(13) = 4(13) – 4 + 13 = 61.

Next, we can evaulate 8&(2&0).

8&(2&0) = 8&(2(0) – 2 + 0)

= 8&(–2) = 8(–2) – 8 + 2 = –22.

Next, let's find 3&(5&2).

3&(5&2) = 3&(5(2) – 5 + 2)

= 3&(7) = 3(7) – 3 + 7 = 25.

Finally, lets evaluate 11&(0&2).

11&(0&2) = 11&(0(2) – 0 + 2)

= 11&(2) = 11(2) – 11 + 2 = 13.

The answer is 11&(0&2).

### Example Question #12 : Evaluating Expressions

x is 75% of y, which is 8 times the amount of 150% of z. What is x in terms of z?

**Possible Answers:**

9z

12z

None of the other answers

6z

7.5z

**Correct answer:**

9z

Just take this step by step. First write out each equation:

x = 0.75y

y = 8(1.5z)

First, simplify the second equation:

y = 12z

Then, substitute y from this equation into the first:

x = 0.75(12z) = 9z

### Example Question #13 : Evaluating Expressions

2x + 6y = 44

What is x + 3y + 33?

**Possible Answers:**

23

81

77

The answer cannot be determined

55

**Correct answer:**

55

The key to solving this question is noticing that we can factor out a two:

2x + 6y = 44 is the same as 2(x + 3y) = 44

Therefore, x + 3y = 22

In this case, x + 3y + 33 is the same as 22 + 33 or 55

### Example Question #14 : Evaluating Expressions

John has four more dollars than four times the amount of dollars that Sandy has.

Peter has three times that of John.

Sandy has $20.

How much money does Peter have?

**Possible Answers:**

64

252

84

288

60

**Correct answer:**

252

Let's make 3 equations based on our data:

J = 4S + 4

P = 3J

S = 20

All we have to do is sequentially replace values.

Substitute 20 for S in the J equation:

J = 4 * 20 + 4 = 84

Now, we can calculate P: P = 3 * 84 = 252

### Example Question #11 : Evaluating And Simplifying Expressions

There are 42 marbles in a bag. Half are red. The remaining ones are green and blue. There are five more blue marbles than green ones. How many marbles are there of each type?

**Possible Answers:**

None of the other answers

21 Red, 13 Blue, 8 Green

21 Red, 16 Blue, 5 Green

4 Red, 15 Blue, 21 Green

21 Red, 8 Blue, 13 Green

**Correct answer:**

21 Red, 13 Blue, 8 Green

Rewrite our question as a set of equations:

R + G + B = 42

R = 42/2 = 21

Therefore, we already know:

G + B = 21

Also, we know that B = 5 + G

Replace that value into the B + G equation:

G + 5 + G = 21 → 2G + 5 = 21 → 2G = 16; G = 8

Therefore, we know that there are 5 + 8 or 13 blue marbles.

The total is therefore 21 Red, 13 Blue, 8 Green

### Example Question #11 : How To Evaluate Algebraic Expressions

The operation x || y is evaluated as: 3x – 14y

What is the value of 5 || (6 || 2)?

**Possible Answers:**

None of the other answers

–235

–10

155

140

**Correct answer:**

155

The operation x || y is evaluated as: 3x – 14y

What is the value of 5 || (6 || 2)?

Do this in parts. Start with 6 || 2:

6 || 2 = 3 * 6 – 14 * 2 = 18 – 28 = –10

This leaves us with:

5 || –10 = 3 * 5 – (14 * –10) = 15 – (–140) = 15 + 140 = 155

### Example Question #12 : Expressions

If the first term of a sequence is 15 and each term is 8 more than the previous term, what is the 24th term of the sequence?

**Possible Answers:**

191

207

199

184

**Correct answer:**

199

Taking 23 terms * 8 = 184; adding the original term of 15 yields 199.

### Example Question #11 : Expressions

If f(x) = 5x/a, and g(x) = ax/10, what is f(2) + g(5)?

**Possible Answers:**

5a

10

(20+a^{2})/2a

a/10

a

**Correct answer:**

(20+a^{2})/2a

(20+a^{2}) / 2a is the answer. Find a common denominator to add the 2 fractions after plugging in the values. So we get 10/a + a/2 after plugging in the values. The lowest common denominator would be 2a. Mutiply 10/a by 2/2, and multiply a/2 by a/a. The new equation appears as 20/2a + a^{2}/2a. Add them together to get (20 + a^{2})/2a.

### Example Question #19 : Evaluating Expressions

(√(4) + √(16))^{2 } = ?

**Possible Answers:**

6

36

√30

√20

20

**Correct answer:**

36

If we use order of operations (PEMDAS), the answer is 36.