### All SAT Math Resources

## Example Questions

### Example Question #1 : Arithmetic

(25 * 10)/(5(6 – 4)^{2})^{ }= ?

**Possible Answers:**

100

25/2

200

25

50

**Correct answer:**

25/2

We use the order of operations, PEMDAS to solve this equation.

(25 * 10)/[5(6 – 4)^{2}]^{ }=

(25 * 10)/[5(2)^{2}]^{ }=

(25 * 10)/[5(4)] =

(25 * 10)/20 =

250/20 = 25/2

### Example Question #2 : Arithmetic

i) add 3z to -2b

ii) multiply by 7

iii) subtract (4z+3b)

What is the result of the above steps in order?

**Possible Answers:**

21z - 14b

25z - 17b

17z - 17b

17z - 11b

**Correct answer:**

17z - 17b

7(3z - 2b) - (4z + 3b) = 17z - 17b

### Example Question #3 : Arithmetic

If L = (9K-11)/(a + 2K), then K =

**Possible Answers:**

(La+2K)/(2L-9)

(2L+aL)/2

(La-7K)/-11

(La+11)/(9-2L)

**Correct answer:**

(La+11)/(9-2L)

First multiply both sides by a + 2K to get rid of the denominator. This gives you Step #1: L (a + 2K) = 9K – 11

Step #2: La + 2KL = 9K – 11. Now put all values with K on one side of the equal sign.

Step #3: La + 11 = 9K – 2KL.

Step #4: La + 11 = K (9 – 2L).

Step #5: (La+11)/(9-2L) = K

### Example Question #4 : Arithmetic

Simplify the result of following the steps below in order.

(1) Subtract 4x from 2y

(2) Multiply that value by 5

(3) Add 2x + y to the product

**Possible Answers:**

22x – 9y

10x – 5y

11y – 18x

30x – 15y

**Correct answer:**

11y – 18x

Remember that when it says subtract from, it should look like 2y – 4x. Multiplying this by 5 = 10y – 20x. 10y – 20x + 2x +y = 11y – 18x.

### Example Question #5 : Arithmetic

Evaluate:

(8^{2 }+ 34/2) ÷ 9 + 1

**Possible Answers:**

33/10

25/10

49/10

10

81/10

**Correct answer:**

10

Order of operations: PEMDAS

Parenthesis/ exponents: (64 + 17) ÷ 9 + 1

(81) ÷ 9 + 1

Division next, so 81 ÷ 9 = 9

9 + 1 = 10

### Example Question #6 : Arithmetic

Solve the problem 1+4/(3-1)-6=

**Possible Answers:**

1

0

-3

2

-1

**Correct answer:**

-3

The order of operations is PEMDAS: Parenthesis, exponents, division and multiplication (performed left to right), addition and subtraction (performed left to right). “Please Excuse My Dear Aunt Sally” is one way to remember the order. One key is that multiplication and division are equal and addition and subtraction are equal, so they are performed in order from left to right.

Step 1. Parenthesis: 1+4/2-6; Step 2. Division 1+2-6; Step 3. Addition/Subtraction: 1+2-6= -3

### Example Question #7 : Arithmetic

Solve 6-(3+2)-4=

**Possible Answers:**

-3

0

3

1

-2

**Correct answer:**

-3

The order of operations is PEMDAS: Parenthesis, exponents, division and multiplication (performed left to right), addition and subtraction (performed left to right). “Please Excuse My Dear Aunt Sally” is one way to remember the order. One key is that multiplication and division are equal and addition and subtraction are equal, so they are performed in order from left to right. Sowe get 6-5-4=-3

### Example Question #8 : Arithmetic

For all positive integers, let *a *★*b* be defined by *a *★*b* = *a**b *^{2}. Which of the following is equal to 8★2?

**Possible Answers:**

1★32

4★2

6★3

3★6

2★4

**Correct answer:**

2★4

To solve this problem, we first evaluate 8★2 and then see which of the answer choices is equal to the resulting number. Using the definition of ★, we see that 8★2 = 8(2^{2}) = 8(4) = 32. The only answer choice that is equivalent to 32 is 2★4, which evaluates to 2(4^{2}) = 32.

(Tip: If we quickly scan the answer choices by squaring the number on the right of the symbol, we immediately see that 3★6 and 1★32 are too big to be 32, even before being multiplied by any of the integers on the left of the symbol.)

### Example Question #1 : How To Find Order Of Operations

Eight more than four is an unknown number less than a quarter of the same unknown number. What is the value of the unknown number?

**Possible Answers:**

0

–16

12

–9

4

**Correct answer:**

–16

Let x be the unknown number.

4 + 8 = 0.25x – x.

12 = –0.75x

x = 12/–0.75

x = –16

### Example Question #10 : Arithmetic

Let a * b be defined as the following:

a * b = b^{2 }– a^{2 }+ ab

Find the value of 4 * (3 * (2 * 1)).

**Possible Answers:**

11

–237

61

101

–11

**Correct answer:**

61

We are told that a * b = b^{2 }– a^{2 }+ ab, and we need to calculate 4 * (3 * (2 * 1)).

We need to start at the innermost set of parantheses, which requires us to find 2 * 1.

2 * 1 = 1^{2} – 2^{2} + 2(1) = 1 – 4 + 2 = –1

We can replace 2 * 1 with negative one. Then our expression becomes.

4 * (3 * (–1))

Now, we must find 3 * (–1)

3 * (–1) = (–1)^{2} – 3^{2} + (3)(–1) = 1 – 9 – 3 = –11

So we can replace 3 * (–1) with –11.

Lastly, we must find 4 * (–11)

4 * (–11) = (–11)^{2} –4^{2} + 4(–11) = 121 – 16 – 44 = 61

The answer is 61.

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