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Unit 1: Number System and Average - Practice Quiz

PEA515 — Analytical Skills-I 60 Questions
0 Correct 0 Wrong 60 Left
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1 Which of the following is a prime number?

Classification of numbers Easy
A. 21
B. 39
C. 35
D. 29

2 Which of the following is an irrational number?

Classification of numbers Easy
A.
B.
C.
D.

3 Which number is divisible by ?

Divisibility rules Easy
A. 124
B. 215
C. 421
D. 327

4 A number is divisible by if its last digit is:

Divisibility rules Easy
A. 6 or 8
B. 2 or 4
C. 0 or 5
D. 1 or 3

5 What is the value of ?

Factorials Easy
A. 12
B. 8
C. 36
D. 24

6 What is the value of ?

Factorials Easy
A. 1
B. 0
C. Undefined
D. 2

7 What is the unit digit of ?

Unit digit calculation Easy
A. 3
B. 7
C. 5
D. 9

8 What is the unit digit of ?

Unit digit calculation Easy
A. 8
B. 2
C. 6
D. 4

9 How many positive factors does have?

Number of factors Easy
A. 5
B. 8
C. 4
D. 6

10 Which number has exactly two positive factors?

Number of factors Easy
A. 8
B. 15
C. 1
D. 11

11 What is the remainder when is divided by ?

Remainder theorem Easy
A. 2
B. 3
C. 4
D. 1

12 If a number is divided by and leaves a remainder of , which statement is correct?

Remainder theorem Easy
A. The number is divisible by
B. The number is less than a multiple of
C. The number is more than a multiple of
D. The number is a multiple of

13 What is the HCF of and ?

HCF and LCM Easy
A. 9
B. 2
C. 6
D. 3

14 What is the LCM of and ?

HCF and LCM Easy
A. 12
B. 24
C. 10
D. 8

15 What is the average of , , and ?

Average calculations Easy
A. 6
B. 5
C. 7
D. 8

16 The average of numbers is . What is their total?

Average calculations Easy
A. 100
B. 15
C. 40
D. 50

17 In a class, students like tea, like coffee, and like both. How many students like tea or coffee?

Inclusion and exclusion Easy
A. 25
B. 35
C. 40
D. 30

18 In a group of people, like cricket and like football. If like both, how many like at least one of the two sports?

Inclusion and exclusion Easy
A. 30
B. 43
C. 23
D. 33

19 A student scores in a test worth and in a test worth . What is the weighted average?

Weighted average Easy
A. 76
B. 74
C. 72
D. 78

20 A shop mixes kg of rice at per kg with kg at per kg. What is the average price per kg?

Weighted average Easy
A. $36
B. $34
C. $38
D. $40

21 Which type of number is ?

Classification of numbers Medium
A. A rational integer
B. A rational non-integer
C. A non-real number
D. An irrational number

22 Which of the following expressions represents a rational number?

Classification of numbers Medium
A.
B.
C.
D.

23 What is the smallest digit such that the number is divisible by ?

Divisibility rules Medium
A.
B.
C.
D.

24 Which digit should replace in so that the number is divisible by ?

Divisibility rules Medium
A.
B.
C.
D.

25 How many trailing zeros are present in ?

Factorials Medium
A.
B.
C.
D.

26 What is the highest exponent of that divides ?

Factorials Medium
A.
B.
C.
D.

27 What is the unit digit of ?

Unit digit calculation Medium
A.
B.
C.
D.

28 What is the unit digit of ?

Unit digit calculation Medium
A.
B.
C.
D.

29 How many positive factors does have?

Number of factors Medium
A.
B.
C.
D.

30 How many positive divisors of are perfect squares?

Number of factors Medium
A.
B.
C.
D.

31 What is the remainder when is divided by ?

Remainder theorem Medium
A.
B.
C.
D.

32 What is the remainder when is divided by ?

Remainder theorem Medium
A.
B.
C.
D.

33 Two positive integers have HCF and LCM . If one integer is , what is the other integer?

HCF and LCM Medium
A.
B.
C.
D.

34 Two numbers are in the ratio , and their HCF is . What is their LCM?

HCF and LCM Medium
A.
B.
C.
D.

35 The average of numbers is . If one of the numbers, , is removed, what is the average of the remaining numbers?

Average calculations Medium
A.
B.
C.
D.

36 The average of numbers increases by when the number is replaced. What is the new number?

Average calculations Medium
A.
B.
C.
D.

37 In a group of students, study Mathematics, study Science, and study both. How many study neither subject?

Inclusion and exclusion Medium
A.
B.
C.
D.

38 Among students, join club , join club , and join club . Also, join both and , join both and , join both and , and join all three. How many join at least one club?

Inclusion and exclusion Medium
A.
B.
C.
D.

39 A class has students with an average score of and students with an average score of . What is the average score of the entire class?

Weighted average Medium
A.
B.
C.
D.

40 A merchant mixes kg of rice costing per kg with kg of rice costing per kg. What is the average cost per kg of the mixture?

Weighted average Medium
A.
B.
C.
D.

41 Classify the number .

Classification of numbers Hard
A. An irrational algebraic number
B. A rational non-integer
C. A transcendental real number
D. A rational integer

42 If the six-digit number is divisible by both and , find .

Divisibility rules Hard
A.
B.
C.
D.

43 What is the greatest integer such that divides ?

Factorials Hard
A.
B.
C.
D.

44 Find the unit digit of .

Unit digit calculation Hard
A.
B.
C.
D.

45 Find the smallest positive multiple of having exactly positive divisors.

Number of factors Hard
A.
B.
C.
D.

46 Find the remainder when is divided by .

Remainder theorem Hard
A.
B.
C.
D.

47 Two positive integers have HCF and LCM . If one of them is , find the other.

HCF and LCM Hard
A.
B.
C.
D.

48 The average of numbers is . Two numbers, and , are replaced by and , respectively. The new average is , and . Find .

Average calculations Hard
A.
B.
C.
D.

49 How many integers from to are divisible by at least one of , , and , but not divisible by ?

Inclusion and exclusion Hard
A.
B.
C.
D.

50 The average score of students is , and that of another students is . What average must additional students obtain for the overall average of all students to be ?

Weighted average Hard
A.
B.
C.
D.

51 Classify the number .

Classification of numbers Hard
A. A rational non-integer
B. A transcendental number
C. An irrational algebraic number
D. A rational integer

52 Find the sum of all numbers of the form that are divisible by .

Divisibility rules Hard
A.
B.
C.
D.

53 How many trailing zeroes does have?

Factorials Hard
A.
B.
C.
D.

54 Find the unit digit of .

Unit digit calculation Hard
A.
B.
C.
D.

55 How many positive divisors of are perfect squares and divisible by ?

Number of factors Hard
A.
B.
C.
D.

56 Find the remainder when is divided by .

Remainder theorem Hard
A.
B.
C.
D.

57 Find the least positive integer such that , , , and .

HCF and LCM Hard
A.
B.
C.
D.

58 The average of values is . If the first values are increased by each and the remaining values are decreased by each, what is the new average?

Average calculations Hard
A.
B.
C.
D.

59 In a group of students, study Mathematics, study Physics, and study Chemistry. Exactly , , and study Mathematics and Physics, Physics and Chemistry, and Chemistry and Mathematics, respectively. If study all three subjects, how many study exactly one subject?

Inclusion and exclusion Hard
A.
B.
C.
D.

60 A mixture contains substance at concentration , substance at concentration , and the remaining portion at concentration . If the mixture concentration is , find .

Weighted average Hard
A.
B.
C. $94.8\%
D.
Next MCQ
Unit 2