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ACT Math : Even / Odd Numbers

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Example Questions

Example Question #1 : How To Multiply Odd Numbers

The product of two numbers is a negative odd integer. Which statement must be true about the numbers?

Possible Answers:

$\textup{Both numbers must be odd.}$

$\textup{Both numbers must be even.}$

$\textup{Both numbers cannot be odd.}$

$\textup{Both numbers must be negative.}$

$\textup{Both numbers must be integers.}$

Correct answer:

$\textup{Both numbers must be odd.}$

Explanation:

For the product of two numbers to be even, one number must be even. For the product of two numbers to be odd, both numbers must be odd.

Remember:

$O \cdot E = E$

$O \cdot O = O$

$E \cdot E = E$

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Example Question #1 : How To Subtract Even Numbers

Evaluate: 102-18

Possible Answers:

Correct answer:

Explanation:

First solve by evaluating the ones digit. Carry over a 1 from the so that the value of the ones digit can be evaluated.

12-8=4

After the carry over, the becomes a . This value will be used for the tens digit of the next term. The hundreds digit will become zero.

Evaluate the tens digit.

9-1=8

Combine the tens digit and the ones digit.

The final answer is .

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Example Question #11 : Even / Odd Numbers

Solve:

128-68

Possible Answers:

Correct answer:

Explanation:

1. First subtract the ones digits:

8-8=0

So the ones digit will be a 0.

2. Next subtract the tens digit borrowing the 1 from the hundreds digit:

12-6=6

So the tens digit will be a 6.

3. Add the tens and ones digits together:

60+0=60

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Example Question #2 : How To Subtract Even Numbers

Solve:

274-88

Possible Answers:

190

186

188

184

Correct answer:

186

Explanation:

1. First subtract the ones digits borrowing a 1 from the tens digit:

14-8=6

So the ones digit will be a 6.

2. Next subtract the tens digit borrowing the 1 from the hundreds digit:

16-8=8

So the tens digit will be a 8.

3. Next add the hundreds, tens and ones digits together:

100+80+6=186

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Example Question #12 : Even / Odd Numbers

Which of the following expressions is odd for any integers and ?

Possible Answers:

5a-3b

2a+3b

4(a+5b+1)

4b-2a+3

All the expressions can be even for some combination of and

Correct answer:

4b-2a+3

Explanation:

The key here is for any integers and , that means that no matter what you set and equal to you will get an odd number. An odd number is not divisible by 2, also it is an even number plus and odd number. The only expression that satisfies this is 4b-2a+3 . will always be even, so will -2a , but is always odd so the combination gives us an odd number, always.

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Example Question #1 : How To Add Even Numbers

Evaluate: 998+1002

Possible Answers:

1996

2810

2016

2000

10982

Correct answer:

2000

Explanation:

For this problem, align and solve by adding the ones digit (8+2) , tens digit $(9+0+ carried\:1)$ , and hundreds digit $(9+carried\:1)$ . This also means that you have to add to the in the thousands place to get .

998+1002=2000

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Example Question #2 : How To Add Even Numbers

Find the sum of 12 and 42.

Possible Answers:

Correct answer:

Explanation:

Rewrite the question into a mathematical expression.

12+42

Add the ones digit.

2+2=4

Add the tens digit.

1+4=5

Combine the tens digit and the ones digit. The answer is .

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Example Question #1 : How To Divide Even Numbers

Solve: $80\div6$

Possible Answers:

14.5

13.3

$\frac{40}{3}$

Correct answer:

$\frac{40}{3}$

Explanation:

This problem can be solved using common factors.

Rewrite $80\div6$ using factors.

$\frac{80}{6}=\frac{2 \cdot 40}{2 \cdot 3} = \frac{40}{3}$

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Example Question #2 : How To Divide Even Numbers

Divide: $1028\div1004$

Possible Answers:

$\frac{257}{251}$

$\frac{6}{5}$

$\frac{267}{256}$

1.023

Correct answer:

$\frac{257}{251}$

Explanation:

Rewrite $1028\div1004$ by using common factors. Reduce to the simplest form.

$\frac{1028}{1004}=\frac{2\cdot 514}{2\cdot 502} = \frac{2\cdot 2\cdot257}{2\cdot 2\cdot251}=\frac{257}{251}$

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Example Question #3 : How To Divide Even Numbers

Divide: $2032\div 234$

Possible Answers:

$\frac{1016}{117}$

$\frac{38}{17}$

$\frac{106}{17}$

8.7

8.6

Correct answer:

$\frac{1016}{117}$

Explanation:

Rewrite $2032\div 234$ and use common factors to simplify.

$\frac{2032}{234}=\frac{2\cdot1016}{2\cdot 117}=\frac{1016}{117}$

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ACT Math : Even / Odd Numbers

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Multiply Odd Numbers

Example Question #1 : How To Subtract Even Numbers

Example Question #11 : Even / Odd Numbers

Example Question #2 : How To Subtract Even Numbers

Example Question #12 : Even / Odd Numbers

Example Question #1 : How To Add Even Numbers

Example Question #2 : How To Add Even Numbers

Example Question #1 : How To Divide Even Numbers

Example Question #2 : How To Divide Even Numbers

Example Question #3 : How To Divide Even Numbers

All ACT Math Resources

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