PSAT Math : Expressions

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%?

50 fl oz

75 fl oz

40 fl oz

85 fl oz

60 fl oz

40 fl oz

Explanation:

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 ?

3&(5&2)

4&(3&4)

8&(2&0)

2&(8&1)

11&(0&2)

11&(0&2)

Explanation:

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.

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?

9z

12z

6z

7.5z

9z

Explanation:

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?

23

81

77

55

55

Explanation:

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?

64

252

84

288

60

252

Explanation:

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?

21 Red, 13 Blue, 8 Green

21 Red, 16 Blue, 5 Green

4 Red, 15 Blue, 21 Green

21 Red, 8 Blue, 13 Green

21 Red, 13 Blue, 8 Green

Explanation:

Rewrite our question as a set of equations:

R + G + B = 42

R = 42/2 = 21

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)?

–235

–10

155

140

155

Explanation:

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

What is the value of 5 || (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?

191

207

199

184

199

Explanation:

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)?

5a

10

(20+a2)/2a

a/10

a

(20+a2)/2a

Explanation:

(20+a2) / 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 + a2/2a. Add them together to get (20 + a2)/2a.

Example Question #19 : Evaluating Expressions

(√(4) + √(16))2  = ?

6

36

√30

√20

20 