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All questions of Unit Digit Calculation for Bank Exams Exam
The digit in the unit place of the number represented by (795 * 358) is- a)7
- b)0
- c)6
- d)4
Correct answer is option 'A'. Can you explain this answer?
The digit in the unit place of the number represented by (795 * 358) is
a)
7
b)
0
c)
6
d)
4
|
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Prakhya Shrivastava answered |
We khow that by increasing power of 7, repeating cycle of 7,9,3,1 respectively comes in unit place... thus at 95 power of 7 unit digit should be 3
i.e.
unit digit of 7^95 = 3
Similarly by increasing power of 3,repeating cycle of 3,9,7,1 respectively comes in unit place hence at 58 power of three unit digit should be 9
i.e.
unit digit of 3^58 = 9
Now unit digit of (7^95 × 3^58) = 3×9 = 27
i.e. 7 is the digit in unit place if we solve (7^95 × 3^58).
Hence option (a) is correct
i.e.
unit digit of 7^95 = 3
Similarly by increasing power of 3,repeating cycle of 3,9,7,1 respectively comes in unit place hence at 58 power of three unit digit should be 9
i.e.
unit digit of 3^58 = 9
Now unit digit of (7^95 × 3^58) = 3×9 = 27
i.e. 7 is the digit in unit place if we solve (7^95 × 3^58).
Hence option (a) is correct
What is the units digit of 3961?- a)9
- b)1
- c)3
- d)7
Correct answer is option 'A'. Can you explain this answer?
What is the units digit of 3961?
a)
9
b)
1
c)
3
d)
7
|
|
Abhishek Phogat answered |
We know that odd power of 9 gives 9 at unit place but even power gives 1 at unit place
Also, 61 is odd hence unit place is 9...
Also, 61 is odd hence unit place is 9...
What is the unit digit in 7105 ?- a)1
- b)5
- c)7
- d)9
Correct answer is option 'C'. Can you explain this answer?
What is the unit digit in 7105 ?
a)
1
b)
5
c)
7
d)
9
|
Rithika Rane answered |
Explanation:
Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]
But, unit digit in (74)26 = 1
Unit digit in 7105 = (1 x 7) = 7Find the unit digit of (7493263)x(15129)- a)3
- b)9
- c)7
- d)1
Correct answer is option 'C'. Can you explain this answer?
Find the unit digit of (7493263)x(15129)
a)
3
b)
9
c)
7
d)
1
|
|
Dipika Gupta answered |
Answer: c)7
Solution:
The given product is (7493263)x(15129)
Required unit digit = the unit digit of(3263)x(129) ...(1)
In the value of 3 to the power 4, we have the unit digit as 1.
so, we can rewrite (3263) = [3(4x65 + 3)] = [(34)65] x (33)
Then from eqn(1),
The unit digit of(3263)x(129) = The unit digit of[(34)65] x (33) x 129
= The unit digit of[165] x 27 x 1
= The unit digit of 1 x 7 x 1 = 7
Hence, the answer is 7.
The given product is (7493263)x(15129)
Required unit digit = the unit digit of(3263)x(129) ...(1)
In the value of 3 to the power 4, we have the unit digit as 1.
so, we can rewrite (3263) = [3(4x65 + 3)] = [(34)65] x (33)
Then from eqn(1),
The unit digit of(3263)x(129) = The unit digit of[(34)65] x (33) x 129
= The unit digit of[165] x 27 x 1
= The unit digit of 1 x 7 x 1 = 7
Hence, the answer is 7.
Find the unit digit of 634262 + 634263- a)0
- b)1
- c)4
- d)6
Correct answer is option 'A'. Can you explain this answer?
Find the unit digit of 634262 + 634263
a)
0
b)
1
c)
4
d)
6
|
Sarthak Mukherjee answered |
Explanation:
To find the unit digit of the given number, we need to find the remainder when the number is divided by 10. The unit digit is the remainder in this case.
Method 1: Using the cyclicity of the unit digits
- We know that the unit digit of any power of 2 repeats in a cycle of 4. The cycle is 2, 4, 8, 6.
- Therefore, to find the unit digit of 634262, we need to find the remainder when 634262 is divided by 4.
- 634262 ÷ 4 = 158565 with a remainder of 2.
- Since the remainder is 2, the unit digit of 634262 is the second digit in the cycle, which is 4.
- Similarly, to find the unit digit of 634263, we need to find the remainder when 634263 is divided by 4.
- 634263 ÷ 4 = 158565 with a remainder of 3.
- Since the remainder is 3, the unit digit of 634263 is the third digit in the cycle, which is 8.
- Therefore, the unit digit of the product 634262 × 634263 is the product of the unit digits of 634262 and 634263, which is 4 × 8 = 32.
- The unit digit of 32 is 2.
Method 2: Using the properties of the unit digits
- The unit digit of 2 raised to any power follows a pattern: 2, 4, 8, 6, 2, 4, 8, 6, ...
- Therefore, the unit digit of 634262 is the same as the unit digit of 2 raised to the power of the unit digit of 634262.
- The unit digit of 634262 is 2, so we need to find the unit digit of 2² = 4.
- Similarly, the unit digit of 634263 is the same as the unit digit of 2 raised to the power of the unit digit of 634263.
- The unit digit of 634263 is 3, so we need to find the unit digit of 2³ = 8.
- Therefore, the unit digit of the product 634262 × 634263 is the product of the unit digits of 634262 and 634263, which is 4 × 8 = 32.
- The unit digit of 32 is 2.
Conclusion:
Using either method, we find that the unit digit of the product 634262 × 634263 is 2. Therefore, the correct answer is option 'A' (0).
To find the unit digit of the given number, we need to find the remainder when the number is divided by 10. The unit digit is the remainder in this case.
Method 1: Using the cyclicity of the unit digits
- We know that the unit digit of any power of 2 repeats in a cycle of 4. The cycle is 2, 4, 8, 6.
- Therefore, to find the unit digit of 634262, we need to find the remainder when 634262 is divided by 4.
- 634262 ÷ 4 = 158565 with a remainder of 2.
- Since the remainder is 2, the unit digit of 634262 is the second digit in the cycle, which is 4.
- Similarly, to find the unit digit of 634263, we need to find the remainder when 634263 is divided by 4.
- 634263 ÷ 4 = 158565 with a remainder of 3.
- Since the remainder is 3, the unit digit of 634263 is the third digit in the cycle, which is 8.
- Therefore, the unit digit of the product 634262 × 634263 is the product of the unit digits of 634262 and 634263, which is 4 × 8 = 32.
- The unit digit of 32 is 2.
Method 2: Using the properties of the unit digits
- The unit digit of 2 raised to any power follows a pattern: 2, 4, 8, 6, 2, 4, 8, 6, ...
- Therefore, the unit digit of 634262 is the same as the unit digit of 2 raised to the power of the unit digit of 634262.
- The unit digit of 634262 is 2, so we need to find the unit digit of 2² = 4.
- Similarly, the unit digit of 634263 is the same as the unit digit of 2 raised to the power of the unit digit of 634263.
- The unit digit of 634263 is 3, so we need to find the unit digit of 2³ = 8.
- Therefore, the unit digit of the product 634262 × 634263 is the product of the unit digits of 634262 and 634263, which is 4 × 8 = 32.
- The unit digit of 32 is 2.
Conclusion:
Using either method, we find that the unit digit of the product 634262 × 634263 is 2. Therefore, the correct answer is option 'A' (0).
The unit digit of the product 1022 x 729 x 889 x 971 is:- a)2
- b)9
- c)1
- d)8
Correct answer is option 'A'. Can you explain this answer?
The unit digit of the product 1022 x 729 x 889 x 971 is:
a)
2
b)
9
c)
1
d)
8
|
|
Debanshi Sarkar answered |
a)2
Solution:
The required answer is the unit digit of the product of the unit digits of the numbers in given product.
i.e, The unit digit of (1022 x 729 x 889 x 971)
= the unit digit of (2 x 9 x 9 x 1)
= the unit digit of (162)
= 2
i.e, The unit digit of (1022 x 729 x 889 x 971)
= the unit digit of (2 x 9 x 9 x 1)
= the unit digit of (162)
= 2
Hence, the answer is 2.
The unit digit in the product (784 x 618 x 917 x 463) is:- a)2
- b)3
- c)4
- d)5
Correct answer is option 'A'. Can you explain this answer?
The unit digit in the product (784 x 618 x 917 x 463) is:
a)
2
b)
3
c)
4
d)
5
|
|
Rithika Rane answered |
Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2
The unit digit of the sum 1289 + 2541 + 8215 + 6137 is:- a)1
- b)2
- c)9
- d)3
Correct answer is option 'B'. Can you explain this answer?
The unit digit of the sum 1289 + 2541 + 8215 + 6137 is:
a)
1
b)
2
c)
9
d)
3
|
|
Rithika Rane answered |
Solution: The required answer is the unit digit of the sum of the unit digits of the numbers in given sum. i.e., The unit digit of (1289 + 2541 + 8215 + 6137) = the unit digit of (9+1+5+7) = the unit digit of (22) = 2 Hence the answer is 2.
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