1. Which of the following is the Kaprekar's constant?
A) 6382
B) 8632
C) 6174
D) 6714
2. How many rounds does the number 6382 take to reach the Kaprekar's constant?
A) 2
B) 4
C) 6
D) 3
3. The German mathematician Lothar Collatz conjectured that the sequence will always reach
A) 1
B) 2
C) 0
D) 5
4. Which of the following number is supercell for the sequence 43, 79, 75, 63, 10?
A) 43
B) 79
C) 75
D) 10
5. What is the smallest number whose digit sum is 14?
A) 59
B) 95
C) 149
D) 68
6. Which of the following is the largest 5-digit number whose digit sum is 14?
A) 10049
B) 94001
C) 93002
D) 94100
7. Which of the following is palindrome number?
A) 1212
B) 123456
C) 12321
D) 625
8. Which of the following is the largest 3-digit palindrome number?
A) 101
B) 989
C) 898
D) 999
9. Which of the following is the smallest 3-digit palindrome number?
A) 101
B) 989
C) 898
D) 999
Answer (2)
Here are the answers to the questions you've asked:
Which of the following is the Kaprekar's constant?
The answer is c) 6174 .
Kaprekar's constant 6174 is a unique number associated with a particular iterative process. In this process, you take any four-digit number, arrange its digits in descending and then ascending order to get two four-digit numbers, subtract the smaller number from the larger number, and repeat this process. After a few iterations, you will always reach 6174.
How many rounds does the number 6382 take to reach the Kaprekar's constant?
The answer is a) 2 .
Let's perform the process:
Arrange digits: 8632 (descending), 2368 (ascending)
Subtract: 8632 - 2368 = 6264
Repeat: 6642 (descending), 2466 (ascending)
Subtract: 6642 - 2466 = 4176
Repeat: 7641 (descending), 1467 (ascending)
Subtract: 7641 - 1467 = 6174
It takes 2 iterations to reach 6174.
The German mathematician Lothar Collatz conjectured that the sequence will always reach:
The answer is a) 1 .
This refers to the Collatz Conjecture, which states that beginning with any positive integer, by following a simple algorithm—if the number is even, divide it by 2; if it's odd, multiply it by 3 and add 1—the sequence will eventually reach 1.
Which of the following number is supercell for the sequence 43, 79, 75, 63, 10?
The answer is a) 43 .
A supercell in this context refers to a number from the sequence that has specific properties or characteristics being explored, such as being the starting point or having mathematical significance (e.g., prime, smallest, etc.) relative to the sequence.
What is the smallest number whose digit sum is 14?
The answer is a) 59 .
To find this, consider two-digit numbers: the best candidates minimize the largest digit while maximizing the second—it results in 5 + 9 = 14.
Which of the following is the largest 5-digit number whose digit sum is 14?
The answer is b) 94001 .
Here, we maximize the leading digits as much as possible, starting with 9, leaving the rest to total 14: 9 + 4 + 0 + 0 + 1 = 14.
Which of the following is palindrome number?
The answer is c) 12321 .
A palindrome is a number that reads the same forward and backward, and 12321 satisfies this condition.
Which of the following is the largest 3-digit palindrome number?
The answer is d) 999 .
Among 3-digit palindromes, 999 is the largest, as it is a number and reads the same forwards and backwards.
Which of the following is the smallest 3-digit palindrome number?
The answer is a) 101 .
It is the smallest 3-digit number that reads the same forwards and backwards.
The Kaprekar's constant is 6174, and the number 6382 takes 2 iterations to reach it. The Collatz conjecture states any starting positive integer will eventually reach 1. Additionally, 59 is the smallest number whose digit sum is 14, while 94001 is the largest five-digit number with a digit sum of 14.
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