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Home › Grade7 › Grade 7 Olympiad › Math Olympiad-Grade-7 › Calculations › Calculations Worksheet-6

Calculations Worksheet-6

Calculations Worksheet-6

 

  1. The digits indicated by * and $ in 3422213*$ so that this number is divisible by 99, are respectively :

(a) 1, 9                (b) 3, 7               (c) 4, 6                (d) 5, 5

 

  1. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y is equal to :

(a) 2                    (b) 3                    (c) 4                    (d) 6

 

  1. How many of the following numbers are divisible by 132 ?

264, 396, 462, 792, 968, 2178, 5184, 6336

(a) 4                    (b) 5                    (c) 6                    (d) 7

 

  1. 6897 is divisible by :

(a) 11 only                                       (b) 19 only        

(c) both 11 and 19                         (d) neither 11 nor 19

 

  1. Which of the following numbers is exactly divisible by all prime numbers between 1 and 17 ?

(a) 345345        (b) 440440       (c) 510510         (d) 515513

 

  1. 325325 is a six–digit number. It is divisible by :

(a) 1 only            (b) 11 only          (c) 11 only          (d) all 7, 11 and 13

 

  1. The number 311311311311311311311 is :

(a) divisible by 3 but not by 11

(b) divisible by 11 but not by 3

(c) divisible by both 3 and 11

(d) neither divisible by 3 nor by 11

 

  1. There is one number which is formed by writing one digit 6 times

(e.g. 111111, 444444 etc.). Such a number is always divisible by :

(a) 7 only           (b) 11 only          (c) 13 only          (d) All of these

 

  1. A 4–digit number is formed by repeating a 2–digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by :

(a) 7                    (b) 11

(c) 13                  (d) smallest 3–digit prime number

 

  1. A six–digit number is formed by repeating a three–digit number; for example, 256256 or 678678 etc. Any number of this form is always exactly divisible by :

(a) 7 only           (b) 11 only          (c) 13 only          (d) 1001

 

  1. The largest natural number which exactly divides the product of any four consecutive natural numbers is :

(a) 6                    (b) 12                  (c) 24                  (d) 120

 

  1. The largest natural number by which the product of three consecutive even natural numbers is always divisible, is :

(a) 16                  (b) 24                 (c) 48                  (d) 96

 

  1. The sum of three consecutive odd numbers is always divisible by :

I. 2             II. 3           III. 5          IV.  6

(a) Only I                                        (b) Only II

(c) Only I and III                          (d) Only II and d I

 

  1. The difference between the squares of two consecutive odd integers is always divisible by :

(a) 3                    (b) 6                    (c) 7                    (d) 8

 

  1. A number is multiplied by 11 and 11 is added to the product. If the resulting number is divisible by 13, the smallest original number is :

(a) 12                  (b) 22                 (c) 26                  (d) 53

 

  1. The sum of the digits of a 3–digit number is subtracted from the number. The resulting number is :

(a) divisible by 6

(b) divisible by 9

(c) divisible neither by 6 nor by 9

(d) divisible by both 6 and 9

 

  1. If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will also be divisible by 11 ?

(a) 4x + 6y         (b) x + y + 4      (c) 9x + 4y         (d) 4x – 9y

 

  1. The largest number that exactly divides each number of the sequence (I5 – 1), (25 – 2), (35 – 3), ....., (n5 – n), ..... is :

(a) 1                     (b) 15                  (c) 30                  (d) 120

 

  1. The greatest number by which the product of three consecutive multiples of 3 is always divisible is :

(a) 54                  (b) 81                  (c) 162                (d) 243

 

  1. The smallest number to be added to 1000 so that 45 divides the sum exactly is :

(a) 10                  (b) 20                 (c) 35                  (d) 80

 

Answer Key:

(1)-(a); (2)-(d); (3)-(a); (4)-(c); (5)-(c); (6)-(d); (7)-(d); (8)-(d); (9)-(d); (10)-(d); (11)-(c); (12)-(c); (13)-(b); (14)-(d); (15)-(a); (16)-(b); (17)-(d); (18)-(c); (19)-(c); (20)-(c)