1.
Which pairs are very similar to Maris–McGwire–Sosa pairs?
Correct Answer
A. Ruth–Aaron pairs
Explanation
Ruth–Aaron pairs are similar to Maris–McGwire–Sosa pairs because they both involve pairs of individuals who achieved significant accomplishments in the same field. In the case of Ruth–Aaron pairs, it refers to pairs of consecutive integers where the sum of the prime factors of each number in the pair is equal. Similarly, Maris–McGwire–Sosa pairs refer to pairs of baseball players who both broke the single-season home run record. Both pairs involve notable achievements and comparisons between individuals in a specific context.
2.
What is the birth name of the mathematician who named the puzzle?
Correct Answer
D. Michael Keith
Explanation
The birth name of the mathematician who named the puzzle is Michael Keith.
3.
How many consecutive natural numbers are used in the puzzle?
Correct Answer
A. 2
Explanation
The puzzle only uses two consecutive natural numbers, which are 2 and 4. The other options 6 and 8 are not consecutive to each other or to any of the other numbers given in the puzzle. Therefore, the correct answer is 2.
4.
The addition of a number's digit—in base 10—to the digits of its prime factorization gives rise to which of the following?
Correct Answer
A. The same sum
Explanation
When we add the digits of a number's prime factorization (in base 10), we are essentially adding the digits of all the prime factors of that number. Since the prime factorization of a number is unique, the sum of the digits in the prime factorization will always be the same for a given number. Therefore, the correct answer is "The same sum."
5.
What is the total number of home runs attained by Mark McGwire and Sammy Sosa?
Correct Answer
D. 62
Explanation
The correct answer is 62 because Mark McGwire and Sammy Sosa both hit a total of 62 home runs.
6.
Are 61 and 62 a Maris–McGwire–Sosa pair?
Correct Answer
A. Yes
Explanation
The given answer "Yes" suggests that 61 and 62 are a Maris-McGwire-Sosa pair. This implies that these two numbers have some significance or connection to the baseball players Maris, McGwire, and Sosa, possibly related to their home run records or achievements. Without further context, it is difficult to determine the exact reason for their classification as a Maris-McGwire-Sosa pair.
7.
What is the formula used for representing the puzzle?
Correct Answer
A. (n, n + 1)
Explanation
The formula used for representing the puzzle is (n, n + 1). This means that the puzzle consists of two consecutive numbers, where n represents the first number and n + 1 represents the second number. This formula allows for a sequential pattern in the puzzle, where each number is one more than the previous number.
8.
Is it possible to have three consecutive integers in this puzzle?
Correct Answer
A. Yes
Explanation
The correct answer is "Yes" because it is possible to have three consecutive integers in the puzzle. Consecutive integers are numbers that follow each other in order without any gaps, such as 1, 2, 3 or -3, -2, -1. Since the question does not specify any restrictions or conditions, it is possible to have three consecutive integers as the answer.
9.
How is m(k) defined?
Correct Answer
B. Smallest integer
Explanation
m(k) is defined as the smallest integer. This means that for any value of k, m(k) will always be the smallest whole number. It will not be a decimal or a fraction, but the smallest whole number possible.
10.
What do we add to each number's digit?
A/an...
Correct Answer
D. Prime number
Explanation
Prime numbers are a set of numbers that are only divisible by 1 and themselves. Adding a prime number to each digit of a number would result in a new number where each digit is increased by that prime number. For example, if we add 2 (a prime number) to each digit of the number 123, we get 345.