Even / Odd Numbers

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PSAT Math › Even / Odd Numbers

Questions 1 - 10
1

Solve:

Explanation

Add the ones digits:

Since there is no tens digit to carry over, proceed to add the tens digits:

The answer is .

2

Solve:

Explanation

Add the ones digits:

Since there is no tens digit to carry over, proceed to add the tens digits:

The answer is .

3

odd * odd * odd =

odd * odd

even * even

even * odd

even * even * even

odd * odd * even

Explanation

The even/odd number properties are good to know. If you forget them, however, it's easy to check with an example.

Odd * odd = odd. If you didn't remember that, a check such as 1 * 3 = 3 will give you the same answer. So if odd * odd = odd, (odd * odd) * odd = odd * odd = odd, just as 3 * 3 * 3 = 27, which is odd. This means we are looking for an answer choice that also produces an odd number. Let's go through them.

even * even = even (2 * 2 = 4)

even * odd = even (2 * 3 = 6)

odd * odd = odd (1 * 3 = 3) This is the correct answer! But just to double check, let's go through the last two.

even * even * even = even * even = even (2 * 2 * 2 = 8)

odd * odd * even = odd * even = even (1 * 3 * 2 = 6)

4

odd * odd * odd =

odd * odd

even * even

even * odd

even * even * even

odd * odd * even

Explanation

The even/odd number properties are good to know. If you forget them, however, it's easy to check with an example.

Odd * odd = odd. If you didn't remember that, a check such as 1 * 3 = 3 will give you the same answer. So if odd * odd = odd, (odd * odd) * odd = odd * odd = odd, just as 3 * 3 * 3 = 27, which is odd. This means we are looking for an answer choice that also produces an odd number. Let's go through them.

even * even = even (2 * 2 = 4)

even * odd = even (2 * 3 = 6)

odd * odd = odd (1 * 3 = 3) This is the correct answer! But just to double check, let's go through the last two.

even * even * even = even * even = even (2 * 2 * 2 = 8)

odd * odd * even = odd * even = even (1 * 3 * 2 = 6)

5

If n is an integer that is not equal to 0, which of the following must be greater than or equal to n?

I. 7n

II. n + 5

III. n2

II only

I and II only

I and III only

II and III only

I, II, and III

Explanation

I is not always true because a negative number multiplied by 7 will give a number that is more negative than the original. II is true because adding 5 to any number will increase the value. III is true because squaring any number will increase the magnitude of the value, and squaring a negative number will make it positive.

6

If n is an integer that is not equal to 0, which of the following must be greater than or equal to n?

I. 7n

II. n + 5

III. n2

II only

I and II only

I and III only

II and III only

I, II, and III

Explanation

I is not always true because a negative number multiplied by 7 will give a number that is more negative than the original. II is true because adding 5 to any number will increase the value. III is true because squaring any number will increase the magnitude of the value, and squaring a negative number will make it positive.

7

If x is an even integer and y is an odd integer. Which of these expressions represents an odd integer?

I. xy

II. x-y

III. 3x+2y

II only

I and II only

II and III only

I and III only

I, II, and III only

Explanation

I)xy is Even*Odd is Even. II) x-y is Even+/-Odd is Odd. III) 3x is Odd*Even =Even, 2y is Even*Odd=Even, Even + Even = Even. Therefore only II is Odd.

8

Theodore has jelly beans. Portia has three times that amount. Harvey has five times as many as she does. What is the total count of jelly beans in the whole group?

Explanation

To find the answer to this question, calculate the total jelly beans for each person:

Portia: * <Theodore's count of jelly beans>, which is or

Harvey: * <Portia's count of jelly beans>, which is or

So, the total is:

(Do not forget that you need those original for Theodore!)

9

If x is an even integer and y is an odd integer. Which of these expressions represents an odd integer?

I. xy

II. x-y

III. 3x+2y

II only

I and II only

II and III only

I and III only

I, II, and III only

Explanation

I)xy is Even*Odd is Even. II) x-y is Even+/-Odd is Odd. III) 3x is Odd*Even =Even, 2y is Even*Odd=Even, Even + Even = Even. Therefore only II is Odd.

10

Theodore has jelly beans. Portia has three times that amount. Harvey has five times as many as she does. What is the total count of jelly beans in the whole group?

Explanation

To find the answer to this question, calculate the total jelly beans for each person:

Portia: * <Theodore's count of jelly beans>, which is or

Harvey: * <Portia's count of jelly beans>, which is or

So, the total is:

(Do not forget that you need those original for Theodore!)

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