Playing With Numbers Worksheet

Multiple Choice Questions

1. The last three 2-digit multiples of 14 are
   (a) 28, 42, 56
   (b) 74, 86, 98
   (c) 14, 28, 42
   (d) 70, 84, 98
   
   
2. The product of the primes of successor of greatest 4-digit number are 
   (a) 3 × 3 × 11 × 11
   (b) 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
   (c) 2 × 2 × 2 × 5 × 5 × 5
   (d) 3 × 3 × 11 × 101
   
   
3. Which of the following is the smallest 3-digit odd composite number?
   (a) 101
   (b) 103
   (c) 105
   (d) 107
   
   
4. The first common multiple of 12 and 14 is
   (a) 24
   (b) 28
   (c) 60
   (d) 84
   
   
5. 59 can be expressed as the sum of any three primes as
   (a) 2 + 17 + 19 + 21
   (b) 17 + 19 + 23
   (c) 5 + 11 + 19 + 23
   (d) 3 + 7 + 19 + 23 
   
   
6. What can be the quotient?
   
   (a) Even number
   (b) zero
   (c) prime number
   (d) composite number
   
   
7. For what natural number ‘m’, 13 + 2m is a prime?
   (a) –1
   (b) 1
   (c) –5
   (d) 5
   
   
8. The sum of all primes between 40 and 60 is
   (a) 243
   (b) 234
   (c) 324
   (d) 343
   
   
9. Product of successor of greatest 3-digit number and HCF of 10 and 16 is 
   (a) 8000
   (b) 4000
   (c) 2000
   (d) 1000
   
   
10. Replace 79?452 by a digit so that the number is divisible by 6.
    (a) 0, 3, 4
    (b) 0, 3, 6, 9
    (c) 3, 5, 6
    (d) 1, 3, 6, 9
    
    
11. (3, 8) are called
    (a) prime numbers
    (b) co-primes
    (c) composite numbers
    (d) even numbers
    
    
12. Every multiple of a given number is
    (a) greater than that number
    (b) less than that number
    (c) greater than or equal to that number
    (d) less than or equal to that number
    
    Subjective Questions
    
    
13. Rani and Kirti were playing puzzle game. Rani wrote one number and put blank in place of one digit and asked Kirti to guess that digit.
    
    When Kirti asked for a hint, Rani said that the number is divisible by 9. Find the missing digit.
    
    
14. Students of class 6 wrote some numbers on board.
    
    Find the numbers which are common multiples of 3 and 4.
    
    
15. Two prime numbers X and Y (X < Y) have LCM as 95. Find the value of 3Y – 2X.
    
    
16. Karan and Sarthak met in a Gym on 7th June. Karan goes to Jim every 3rd day and Sarthak goes every 5th day. On what day of June will they meet again? 
    
    
17. Guess the number!
    
    
    
    
18.  Check whose birthdate is divisible by 3.
    
    
    
19. Shweta has 131 balloons. She wants to distribute 5 balloons to each of her classmate to blow. But, when she started distributing, one of her classmate got less than 5 balloons. How many more balloons are needed so that everyone gets 5 balloons?
     
20. A shop-owner wants to pack 24 kg of sugar, 18 kg of dal and 48 kg of wheat in bags in such a manner that each bag should have equal number of kgs and of the same kind. How many kgs should be put in a single bag and how many bags would he need?

Multiple Choice Questions

1. The last three 2-digit multiples of 14 are
   (a) 28, 42, 56
   (b) 74, 86, 98
   (c) 14, 28, 42
   (d) 70, 84, 98
   Correct option: (d) 70, 84, 98
   Solution:
   2-digit multiples of 14 are 14, 28, 42, 56, 70, 84, and 98.
   Hence, the last three 2-digit multiples of 14 are 70, 84, 98.
   
   
2. The product of the primes of successor of greatest 4-digit number are 
   (a) 3 × 3 × 11 × 11
   (b) 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
   (c) 2 × 2 × 2 × 5 × 5 × 5
   (d) 3 × 3 × 11 × 101
   Correct option: (b) 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
   Solution:
   Greatest 4-digit number = 9999
   Successor of 9999 = 9999 + 1 = 10000
   Prime factorisation of 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
   
   
3. Which of the following is the smallest 3-digit odd composite number?
   (a) 101
   (b) 103
   (c) 105
   (d) 107
   Correct option: (c) 105
   Solution:
   A number which has more than two different factors is called a composite number.
   
   
4. The first common multiple of 12 and 14 is
   (a) 24
   (b) 28
   (c) 60
   (d) 84
   Correct option: (d) 84
   Solution:
   Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96,…
   Multiples of 14 = 14, 28, 42, 56, 70, 84, 98,…
   First common multiple of 12 and 14 is 84.
   
   
5. 59 can be expressed as the sum of any three primes as
   (a) 2 + 17 + 19 + 21
   (b) 17 + 19 + 23
   (c) 5 + 11 + 19 + 23
   (d) 3 + 7 + 19 + 23
   Correct Option: (b) 17 + 19 + 23
   Solution:
   59 = 17 + 19 + 23 (Sum of three primes)
   
   
6. What can be the quotient?
   
   (a) Even number
   (b) zero
   (c) prime number
   (d) composite number
   Correct option: (c) prime number
   Solution:
   51 ÷ 17 = 3, which is a prime number
   
   
7. For what natural number ‘m’, 13 + 2m is a prime?
   (a) –1
   (b) 1
   (c) –5
   (d) 5
   Correct option: (d) 5
   Solution:
   Since ‘m’ is a natural number, m can be either 1 or 5.
   For m = 1, 13 + 2(1) = 13 + 2 = 15, which is not a prime.
   For m = 5, 13 + 2(5) = 13 + 10 = 23, which is a prime.
   
   
8. The sum of all primes between 40 and 60 is
   (a) 243
   (b) 234
   (c) 324
   (d) 343
   Correct option: (a) 243
   Solution:
   Primes between 40 and 60 = 41, 43, 47, 53, 59
   Required sum = 41 + 43 + 47 + 53 + 59 = 243
   
   
9. Product of successor of greatest 3-digit number and HCF of 10 and 16 is 
   (a) 8000
   (b) 4000
   (c) 2000
   (d) 1000
   Correct Option: (c) 1000
   Solution:
   Successor of greatest 3-digit number = 999 + 1 = 1000
   HCF of 10 and 16 = 2
   Required product = 1000 × 2 = 2000
   
   
10. Replace 79?452 by a digit so that the number is divisible by 6.
    (a) 0, 3, 4
    (b) 0, 3, 6, 9
    (c) 3, 5, 6
    (d) 1, 3, 6, 9
    Correct option: (b) 0, 3, 6, 9
    Solution:
    A number is divisible by 6 if it is divisible by 2 as well as by 3.
    Now, for a number to be divisible by 2, the unit’s digit should be 0, 2, 4, 6, 8.
    The given number already has unit’s digit as 2.
    And, for a number to be divisible by 3, the sum of the digits of a number should be divisible by 3.
    Sum of digits = 7 + 9 + ? + 4 + 5 + 2 = 27 + ?
    So, missing digit can be 0 or 3 or 6 or 9 to be divisible by 3.
    
    
11. (3, 8) are called
    (a) prime numbers
    (b) co-primes
    (c) composite numbers
    (d) even numbers
    Correct option: (b) co-primes
    Solution:
    The numbers which have only 1 as a common factor are called co-primes.
    
    
12. Every multiple of a given number is
    (a) greater than that number
    (b) less than that number
    (c) greater than or equal to that number
    (d) less than or equal to that number
    Correct option: (c) greater than or equal to that number
    Solution:
    Every multiple of a given number is greater than or equal to that number.|
    For example, multiples of 6 = 6, 12, 18, 24 and so on.
    
    Subjective Questions
    
    
13. Rani and Kirti were playing puzzle game. Rani wrote one number and put blank in place of one digit and asked Kirti to guess that digit.
    
    When Kirti asked for a hint, Rani said that the number is divisible by 9. Find the missing digit.
    Solution:
    If a number is divisible by 9, then the sum of the digits of a number is also divisible by 9.
    Now, the sum of the digits of given number = 4 + 1 + 0 + * + 0 + 7 = 12 + 0
    To make the number divisible by 9, the * can be replaced by 6.
    So, sum of the digits = 12 + 6 = 18, which is divisible by 9.
    
    
14. Students of class 6 wrote some numbers on board.
    
    Find the numbers which are common multiples of 3 and 4.
    Solution:
    Common multiples of 3 and 4 are 36, 48, 24 and 12.
    
    
15. Two prime numbers X and Y (X < Y) have LCM as 95. Find the value of 3Y – 2X.
    Solution:
    Prime factors of 95 are 5 and 19.
    Then, let us say LCM of 5 and 19 is 95.
    ⇒ X = 5 and Y = 19 (X < Y)
    ∴ 3Y – 2X = 3(19) – 2(5) = 57 – 10 = 47
    
    
16. Karan and Sarthak met in a Gym on 7th June. Karan goes to Jim every 3rd day and Sarthak goes every 5th day. On what day of June will they meet again? 
    Solution:
    LCM of 3 and 5 = 15
    Now, the day of the month they will meet again = 7 + 15 = 22.
    Therefore, they will be meet again on 22^nd June.
    
    
17. Guess the number!
    
    
    Solution:
    A number is divisible by 8, if its last three digits are divisible by 8.
    The last two digits are given as 56 and hundred’s place is the least whole number, which is 0.
    So, the last 3 digits are 056, which are divisible by 8.
    Now, first 4 digits are LCM of 4, 7, 9 and 10.
    4 = 2 × 2
    7 = 1 × 7
    9 = 3 × 3
    10 = 2 × 5
    LCM = 2 × 2 × 3 × 3 × 5 × 7 = 1260
    So, the required number is 1260056.
    
    
18.  Check whose birthdate is divisible by 3.
    
    Solution:
    A number is divisible by 3 if the sum of the digits of a number is divisible by 3.
    Reema = 1/09/2012 = 1 + 0 + 9 + 2 + 1 + 2 = 15, divisible by 3
    John = 5/01/2011 = 5 + 0 + 1 + 2 + 0 + 1 + 1 = 10, not divisible by 3
    Nikita = 10/10/2012 = 1 + 0 + 1 + 0 + 2 + 0 + 1 + 2 = 7, not divisible by 3
    Julie = 3/05/2011 = 3 + 0 + 5 + 2 + 0 + 1 + 1 = 12, divisible by 3
    Therefore, birthdates of Reema and Julie are divisible by 3.
    
    
19. Shweta has 131 balloons. She wants to distribute 5 balloons to each of her classmate to blow. But, when she started distributing, one of her classmate got less than 5 balloons. How many more balloons are needed so that everyone gets 5 balloons?
    Solution:
    For a number to be divisible by 5, the digit at the unit’s place should be either 0 or 5.
    131 has 1 at the unit’s place.
    To make it divisible by 5, we need to add 4 to it.
    ⇒ 131 + 4 = 135, which is divisible by 5
    Hence, 4 more balloons are needed.
    
    
20. A shop-owner wants to pack 24 kg of sugar, 18 kg of dal and 48 kg of wheat in bags in such a manner that each bag should have equal number of kgs and of the same kind. How many kgs should be put in a single bag and how many bags would he need?
    Solution:
    20.Here, we need to find HCF of 24, 18 and 48.
    24 = × 2 × 2 ×
    18 =  ×  × 3
    48 =  × 2 × 2 × 2 × 
    HCF = 2 × 3 = 6
    Total grocery = 24 kg + 18 kg + 48 kg = 90 kg
    And, 90 ÷ 6 = 15
    Therefore, 6 kgs should be put in a single bag and 15 such bags would be needed.