## Example Questions

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### Example Question #1 : Arithmetic

(25 * 10)/(5(6 – 4)2) = ?

25

25/2

50

100

200

25/2

Explanation:

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

ii) multiply by 7

iii) subtract (4z+3b)

What is the result of the above steps in order?

25z - 17b

17z - 17b

21z - 14b

17z - 11b

17z - 17b

Explanation:

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

### Example Question #3 : Arithmetic

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

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

(La-7K)/-11

(2L+aL)/2

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

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

Explanation:

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

10x – 5y

22x – 9y

30x – 15y

11y – 18x

11y – 18x

Explanation:

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:

(82  + 34/2) ÷ 9 + 1

10

25/10

49/10

81/10

33/10

10

Explanation:

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=

-3

0

-1

1

2

-3

Explanation:

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=

1

3

-2

-3

0

-3

Explanation:

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 = ab 2. Which of the following is equal to 8★2?

6★3

4★2

1★32

2★4

3★6

2★4

Explanation:

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(22) = 8(4) = 32. The only answer choice that is equivalent to 32 is 2★4, which evaluates to 2(42) = 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 #9 : Arithmetic

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?

12

4

–9

0

–16

–16

Explanation:

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– a+ ab

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

–237

101

11

61

–11

61

Explanation:

We are told that a * b = b– a+ 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 = 12 – 22 + 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 – 32 + (3)(–1) = 1 – 9 – 3 = –11

So we can replace 3 * (–1) with –11.

Lastly, we must find 4 * (–11)

4 * (–11) = (–11)2 –42 + 4(–11) = 121 – 16 – 44 = 61 