Problems on Numbers - Handout 4

 

1.Find the unit digit of (1173+2345+680+34+77)

a)5                   b)6              c)9               d)7

2.What is the unit’s digit in the product of all prime numbers except 2?

a)1                   b)5              c)7               d)8    

3.The unit digit in the sum of (4387)²⁴⁵ + (621)⁷² is

a)1                   b2                c)5               d)8

4.The unit digit in the product (122)¹⁷³ is

a)2                   b)4              c)6               d)8

5.The last digit of (2001)²⁰⁰⁸ + 2002 is

a)0                   b)3               c)4               d)6

6.The digit in the unit’s place of

 [251⁹⁸ +21²⁹-106¹⁰⁰+705³⁵-16⁴ +259]

a)1                   b)4               c)6               d)8

7.What is the unit digit of 666⁹⁹⁹ + 999^666?

a)7                   b)9              c)6               d)5

8.The digit in the unit’s place of the product (71 x 72 x 73 x …x 79) is

a)2                    b)0              c)6               d)8

9.Two numbers are such that their sum is 16 and their product is 55. Find the sum of their reciprocals?

a)16/55   b) 14/55                 c) 18/55     d) 17/55

10.Two positive integers differ by 4, and the sum of their reciprocals is 10/21. Then find the larger number?

a)3                      b)5           c)7               d)9

11.The reciprocal of the sum of the reciprocals of 3/5 and 5/7 is

a)2/3       b)5/12                   c)15/46                  d)4

12.One-third of three-fifth of a number is 21. What is the number?

a)  105              b) 85            c)65      d) 75

13.If two-fifth of one-fourth of a number is 18, then what is the sum of the two digits of the number?

a) 40                 b) 9             c) 4      d) 1

14.If one-eighth of a number increased by 5 is 8, then what is the number?

a)75           b) 25         c) 30            d) 24

15.If 10 be added to 4 times a certain number, the result is 5 less than 5 times the number,then the number is:

a)15        b)20             c)25             d)35

16.Find the number which, when multiplied by 15, is increased by 280. 

 a)18       b)15              c)30            d)20

17.Which one of the following numbers will completely divide (5⁷¹+5⁷² +5⁷³)?

a)   155    b)150           c)160           d)30

18.(4⁶¹ + 4⁶² + 4⁶³) is divisible by

a)3                   b)11             c)13             d)17

19.If a and b are odd numbers, then which of the following is even?

a)a+b+ab b)a+b-1                 c)a+b+1d)a+b+2ab

20.If a is even number and b is an odd number, then which of the following is odd?

a)(5a-2b)²         b) (a+2b)     c)3a-2b         d) (a+b)²

21.If n is even, (6ⁿ-1) is divisible by

a)37        b)35             c)30             d)6

22.If m and n are positive integers and (m-n) is an even number, then (m² -  n²) is always divisible by

a)4                   b)6              c)8               d)12

23.If a and b are two odd positive integers, by which of the following integer is (a⁴-b⁴) always divisible

a)3                   b)6              c)8               d)12

24.If n be any natural number, then by which the largest number (n³-n) is always divisible?

a)3                   b)6              c)12             d)18

25.The greatest whole number, by which the expression (n⁴+6n³+11n²+6n+24) is divisible for every natural number n, is

a)6                   b)24             c)12             d)48

26.Find the largest number, which exactly divides every number of the form (n³ – n) (n-2) where n is a natural number greater than 2

a)6                   b)12             c)24             d)48