If n + 12 is a positive odd integer, which of the following must be true about the sum of the next four integers?a)It is a multiple of 3b)It is a multiple of 4c)It is a prime numberd)It is a multiple of 5e)It is a multiple of 2Correct answer is option 'E'. Can you explain this answer?

Question

Answer

If n + 12 is a positive odd integer, it means that n is an odd integer. Let's consider the next four integers after n.

The four consecutive integers after n can be represented as n + 1, n + 2, n + 3, and n + 4.

Since n is odd, all four consecutive integers will be odd as well, as adding an even number to an odd number results in an odd number.

The sum of two odd numbers is always an even number. Therefore, the sum of n + 1, n + 2, n + 3, and n + 4 will be an even number.

Hence, the correct answer is E: It is a multiple of 2.

Answer

Explanation:

Given: n + 12 is a positive odd integer

Key Points:
- A positive odd integer can be represented as 2k + 1, where k is an integer
- n + 12 = 2k + 1 (positive odd integer)

Next Four Integers:
- The next four integers after n + 12 are n + 13, n + 14, n + 15, and n + 16

Analysis:
- n + 13 is the next integer after n + 12, which is one more than a positive odd integer
- n + 14, n + 15, and n + 16 are consecutive integers following n + 13

Explanation:
- The sum of the next four integers would be (n + 13) + (n + 14) + (n + 15) + (n + 16)
- Simplifying this expression gives 4n + 58

Conclusion:
- Since 4n is always even for any integer n, adding 58 (even number) to an even number will always result in an even number
- Therefore, the sum of the next four integers must be even, making it a multiple of 2
Therefore, the correct answer is option 'e) It is a multiple of 2'.

Similar GMAT Doubts

If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer?

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

The function f(m) is defined for all positive integers m as the product of m + 4, m + 5, and m + 6. If n is a positive integer, then f(n) must be divisible by which one of the following numbers?

In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be

For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2. What is the sum of all the even integers be tween 99 and 301?

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

Top Courses for GMAT

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams