unitarydigits

1. What could be the units digit of 22n, where n is an integer.

A.1
B.2
C.3
D.4
E.5
F.6
G.8

2. Find the units digit of 4342

A.0
B. 2
C.4
D. 6
E. 8

3. What is the unit digit of 11x22X33 X.......99?

A. 0
B. 1
C. 2
D. 3
E. 5

4. What could be the units digit of 19473n

A.0
B.1
C.2
D.3
E.6
F.8
G.9

5.What is the unit digit of 93n+5, n is a prime number greater than 5.

6.Find the units digit of 10011+10022+10033+.......10099?

A.0
B. 1
C. 2
D. 3
E. 7

7. What could be the units digit of 9nX 22n, where n is an integer?

A.2
B.3
C.6
D.11
E.13
F.15
G.17

8.Find the units digit of 11X33X55X77X.......9797X9999

A. 0
B. 1
C. 2
D. 3
E. 5

9. abcd is a four digit number. Find the value of d if the units digit of (abcd)15 is 6

A. 2
B. 4
C. 6
D. 8
E. 9

10. abcd is a four digit number. What could be the value of d if the units digit of (abcd)12 is 6

A. 1
B. 2
C. 4
D. 6
E. 8
F. 9

11. 172271 has a units digit of:

12.a,b are single digit positive integers. If the units digit of ab+ba=6,then find the value of (a+b).

A. 6
B. 8
C. 10
D. 12
E. 14

13.11+22+33+...+100100 is divided by 2. What is the remainder?

A. 0
B. 1
C.2
D. 3
E. 4

14.What is the units digit of (71)5(46)3(103)4 + (57)(1088)3 ?

A. 0
B. 1
C. 2
D. 3
E. 4

15. What is the units digit of 17728 – 13323?

A. 1
B. 3
C. 4
D. 6
E. 9

16. If a,b are two positive integers which of the following must be true.

A. 5a+6b is even
B. 8a+6b is odd
C. 5a+7b is odd
D. 7a+6b is divisible by2.
E. 5a+6b is odd.

17.How many zeroes does 20020 have?

A. 40
B. 48
C. 49
D. 51
E. 54

18. What is the first non-zero digit that the number 20020has from the right?

A. 0
B. 1
C. 2
D. 3
E. 6

19. What is the units digit of 292008-181996?

A. 0
B. 3
C. 5
D. 11
E. 13

20.What is the units digit of 292008+181996?

A. 6
B. 7
C. 9
D. 12
E. 15


Explanation for Question1:

What could be the units digit of 22n, where n is an integer.


Answer – (C) Solution: 22n is nothing but 2even
2even ends with either 4 or 6.

Find the units digit of 4342

Answer – (C) Solution:
4342 is nothing but 4odd.
4odd always ends with 4.

What is the unit digit of 11x22X33 X.......99


Answer – (A) Solution: 11x22X33 X.......99 consists 55
55 ends with 5.
Multiples of 5 either end with 0 or 5.
5 multipled with even numeber always end with zero.
So the answer is 0.
Explanation for Question 4:

What could be the units digit of 19473n

Solution:
the units digit of 19473n is same as the units digit of 73n
when n=1, the units digit of 73=3
when n=2, the units digit of 76=9
when n=3, the units digit of 79=7
when n=4, the units digit of 712=1

5.What is the unit digit of 93n+5, n is a prime number greater than 5..

Answer:6
Solution: Any prime number greater than 5 is always odd.
therefore 3n is odd
3n+5 is even.
93n+5=9even,which always ends with 1.
Explanation for Question 6:

.Find the units digit of 10011+10022+10033+.......10099?


Answer – The units digit of11=1
The units digit of22=4
The units digit of33=7
The units digit of44=6
The units digit of55=5
The units digit of66=6
The units digit of77=3
The units digit of88=6
The units digit of99=9
Sum of the units digit =47
Explanation for Question 7:

What could be the units digit of 9nX 22n, where n is an integer?

Answer :By plugging n=1,2,3...in 9nX 22n,it always ends with 6.
Explanation for Question8:

Find the units digit of 11X33X55X77X.......9797X9999

Answer:55 ends with 5.
Multiples of 5 either end with 0 or 5.
5 multipled with odd numeber always end with 5.
So the answer is 5.
Explanation for Question9:

abcd is a four digit number. Find the value of d if the units digit of (abcd)15 is 6?

Answer-by verifying the options d= 6 satisfies. so the answer is 6.
Explanation for Question 10: abcd is a four digit number. What could be the value of d if the units digit of (abcd)12 is 6
Solution:By verifying the optios d=2,4,6,8 satisfies.
Explanation for Question 11:

172271 has a units digit of:


Answer – 8
Solution: the units digit of 172271 is equal to 2271
2271 is in the form of 24n+3,which end with 8.So the answer is 8.
Explanation for Question 12:

a,b are single digit positive integers. If the units digit of ab+ba=6,then find the value of (a+b).

. Solution: The only combination satisfies is 5,1. Hence the answer is 6.
Explanation for Question 13:11+22+33+...+100100 is divided by 2. What is the remainder?
Explanatory Answer
11+22+33+...+100100 is even.
When even number is divided by 2 it leaves a remainder 0.
Explanation for Question 14:What is the units digit of (71)5(46)3(103)4 + (57)(1088)3
Explanatory Answer
The units digit of 715=7
The units digit of 463=6
The units digit of 1034=1
The units digit of(71)5(46)3(103)4 = 1 x 6 x 1=6---------> (i)
The units digit of 10883=2
The units digit of (57)(1088)3= 7 x 2 =4---------->(ii)
adding (i) and (ii) the answer is 0.
Explanation for Question 15
What is the units digit of 17728 – 13323?
Explanatory Answer
the units digit of 17728=1
the units digit of 13323=7
1-7=4 ( 17728 is greater than 13323)
Explanation for Question 16: If a,b are two positive integers which of the following must be true.
Solution:A:
A. 5a+6b is even :5a is odd,6b is even
odd+even=odd, option A is ruled out.
B. 8a+6b is odd:8a is even,6b is even
even+even=even, option B is ruled out.
C. 5a+7b is odd:5a is odd,7b is odd
odd+odd=even, option C is ruled out.
D. 7a+6b is divisible by2.:7a is odd,6b is even
odd+even=odd, which is not divisible by 2.
E. 5a+6b is odd. 5a is odd,6b is even
odd+even=odd, option E is the correct.
Explanation for Question 17:

How many zeroes does 20020 have?

Explanatory Answer 20020=220x10020
10020 ends with 40 zeroes.
Explanation for Question 18: What is the first non-zero digit that the number 20020has from the right?
Explaination: 20020=220x10020
220 ends with 6.
the first non-zero digit in 20020 is 6.
Explanation for Question 19: What is the units digit of 292008-181996
Explaination:the units digit of 292008=1
the units digit of181996 is 6.
292008 is greater than 181996
11-6=5(1 carring 1 from the prevous digit 1 will become 11)
Explanation for Question 20: What is the units digit of 292008-181996
Explaination:the units digit of 292008=1
the units digit of181996 is 6.
292008 is greater than 181996
1+6=7.
S-BATCH