PSAT Math : Arithmetic

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #12 : How To Find The Greatest Or Least Number Of Combinations

For a certain lunch special, customers must order a salad, an entree, and a dessert. If there are three different salads, four different entrees, and two different desserts available, then how many different lunch specials are possible?

Possible Answers:

18

9

12

24

72

Correct answer:

24

Explanation:

Customers must choose a salad, an entree, and a dessert. There are three different salads, four entrees, and two desserts.

The simplest way of determining the number of combinations is by multiplying the number of options for each part of the meal. In other words, we can find the product of 3, 4, and 2, which would give us 24.

Sometimes, if you can't think of a way to mathetimatically determine all of the different combinations of something, it helps to write out as many as you can. Let's write out all of the possible cominbations just to verify that there are 24. Let's call the different salads S1, S2, and S3. We will call the four entrees E1, E2, E3, and E4, and we will call the desserts D1 and D2.

Here are the possible lunch special combinations:

S1, E1, D1

S1, E1, D2

S1, E2, D1

S1, E2, D2

S1, E3, D1

S1, E3, D2

S1, E4, D1

S1, E4, D2

S2, E1, D1

S2, E1, D2

S2, E2, D1

S2, E2, D2

S2, E3, D1

S2, E3, D2

S2, E4, D1

S2, E4, D2

S3, E1, D1

S3, E1, D2

S3, E2, D1

S3, E2, D2

S3, E3, D1

S3, E3, D2

S3, E4, D1

S3, E4, D2

The answer is 24.

Example Question #1721 : Sat Mathematics

There are five pictures but only four display cases.  The display cases are unique. How many different arrangements of pictures in display cases can be created?

Possible Answers:

120

50

5

24

240

Correct answer:

120

Explanation:

There are five possible choices for the first space. For the second there are four possible, three for the third, and two for the fourth. 5 * 4 * 3 * 2 = 120 possible arrangements.

Example Question #11 : How To Find The Greatest Or Least Number Of Combinations

The art club must choose a leadership committee of 3 students.  If any

member can be on the committee, how many different combnations of 3

students can be selected from the 15 members of the art club?

Possible Answers:

Correct answer:

Explanation:

Example Question #1892 : Psat Mathematics

A company assigns employee numbers according to the following scheme:

1) Each number must comprise three letters, followed by five numerals.

2) The first numeral must be either '1' or '2'; there are no other restrictions on the numerals.

3) There cannot be repetition among the three letters.

4) To prevent confusion with the numerals '1' and '0', the letters 'I' and 'O' cannot appear.

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, none of which are 'I' or 'O', meaning that three letters will be selected from a set of 24. Also, order will be important, so the number of ways to choose this group of three will be .

The letters are followed by either a '1' or a '2', so this makes 2 possibilities.

The next three characters will be numerals, and 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 #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:

17

16

18

14

15

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 #341 : Arithmetic

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 #1 : 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 .

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