PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #131 : Integers

A company assigns employee numbers according to the following scheme:

1) Each number must comprise three letters, followed by four numerals, followed by one letter.

2) There are no restrictions on the numerals.

3) There cannot be repetition among the first three letters; however, the final letter can be any letter, even if that letter is among the first three.

Which of the following expressions is equal to the number of possible employee numbers?

Possible Answers:

Correct answer:

Explanation:

The first three characters must be distinct letters, meaning that three letters will be selected from a set of 26. Also, order will be important, so the number of ways to choose this group of three will be .

The next four characters will be numerals, with no restrictions, so the number of ways to choose this group will be 

The last character can be any of 26 letters.

By the multiplication principle, the number of ways to choose an employee number will be

Example Question #1 : How To Find Permutation Notation

A company assigns employee numbers according to the following scheme:

1) Each number must comprise two letters, followed by four numerals, followed by two letters.

2) There are no restrictions on the numerals.

3) There cannot be repetition between the first two letters.

4) There cannot be repetition between the last two letters.

5) A letter appearing as one of the first two letters can appear as one of the last two.

Which of the following expressions is equal to the number of possible employee numbers?

Possible Answers:

Correct answer:

Explanation:

The first two characters must be distinct letters, meaning that two letters will be selected from a set of 26. Also, order will be important, so the number of ways to choose this group of two will be .

Similarly, since the last two characters will be chosen according to the same rule, with repetition allowed between the two groups, there will be  ways to choose them as well.

The next four characters will be numerals, but there will be no restrictions, so the number of ways to choose this group will be .

By the multiplication principle, the number of ways to choose an employee number will be

Example Question #1 : How To Find The Number Of Integers Between Two Other Integers

A custom-made ruler is 30\ cm long and for every 2\ cm there's a tick mark. How many tick marks are there on the ruler?

Possible Answers:

16

14

18

15

17

Correct answer:

16

Explanation:

There will be 15 gaps of 2\ cm long but 16 tick marks because there will be a tick mark on each end of the ruler.

Example Question #1711 : Sat Mathematics

How many prime numbers are between 1 to 25?

Possible Answers:

Correct answer:

Explanation:

A prime numbers is a number greater than 1 that can only be divided by 1 and itself. Simply count from 1 to 25 and see how many values fit the criteria.

2, 34, 56, 78, 9, 10, 1112, 1314, 15, 16, 1718, 19, 20, 21, 22, 2324, 25

Prime numbers are underlined. Nine prime numbers are in this set interval.

Example Question #181 : Integers

Four consecutive odd integers sum to 40. How many of these numbers are prime?

Possible Answers:

Correct answer:

Explanation:

Let x equal the smallest of the four numbers. Therefore:

\dpi{100} x + (x+2)+(x+4)+(x+6)=40

\dpi{100} 4x +12 = 40

\dpi{100} 4x + 28

\dpi{100} x=7

Therefore the four odd numbers are 7, 9, 11, and 13. Since all are prime except 9, three of the numbers are prime.

Example Question #2 : How To Find The Number Of Integers Between Two Other Integers

Find the median of this set of numbers

Possible Answers:

Correct answer:

Explanation:

To find the median of a set of numbers, we must first order them from smallest to greatest.

Next, we must find the number directly in the middle, which has an equal number of numbers to the right and to the left.

Therefore, our answer is .

Example Question #1 : How To Find The Missing Number In A Set

Which number completes the following series: 1, 2, 4, 8, 16, 32, 64, _?

Possible Answers:

Not enough information

16

64

128

15

Correct answer:

128

Explanation:

All of the numbers in this series are 2n-1. The number that we are looking for is the eighth number. So 28–1 = 27 = 128.

Example Question #2 : How To Find The Missing Number In A Set

Alhough Danielle’s favorite flowers are tulips, she wants at least one each of three different kinds of flowers in her bouquet. Roses are twice as expensive as lilies and lilies are 25% of the price of tulips. If a rose costs $20 and Danielle only has $130, how many tulips can she buy?

Possible Answers:

4

3

2

5

1

Correct answer:

2

Explanation:

She can only buy 2 tulips at $80, because if she bought 3 she wouldn’t have enough to afford the other 2 kinds of flowers.  She has to spend at least 30 dollars (20 + 10) on 1 rose and 1 lily.

Example Question #1 : How To Find The Missing Number In A Set

Which of the following is not a rational number?

Possible Answers:

5

1.75

√2

0.111...

.001

Correct answer:

√2

Explanation:

A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational. 

5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9

√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi. 

Example Question #2 : Sets

Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?

Possible Answers:

\dpi{100} \small \left \{0,2,3,5,6,7,8 \right \}

\dpi{100} \small \left \{1,3,4,5,7,9 \right \}

\dpi{100} \small \left \{ 0,1,2,3,4,5,6,7,8,9 \right \}

\dpi{100} \small \left \{1,2,3,4,5,6,7,8,9 \right \}

\dpi{100} \small \left \{2,3,4,5,6,7,8,9 \right \}

Correct answer:

\dpi{100} \small \left \{ 0,1,2,3,4,5,6,7,8,9 \right \}

Explanation:

The prime digits are 2, 3, 5, and 7.

The perfect square digits are 0, 1, 4, and 9.

The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.

Learning Tools by Varsity Tutors