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DIRECTIONS for the question: Solve the following question and mark the best possible option.
Q. The only way that 10 can be written as the sum of 4 different natural numbers is 1 + 2 + 3 + 4. In how many different ways can 15 be written as the sum of 4 different natural numbers?
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Case 1: If we take the first two numbers as 1 and 2, then the sum of the third and fourth number has to be 12. Cases possible are
 ► 3, 9 
 ► 4, 8  
 ► 5, 7
Case 2: If we take the first two numbers as 1 and 3, then the sum of the third and fourth number has to be 11. Cases possible are
 ► 4, 7 
 ► 5, 6  
Case 3: If we take the first number as not 1
Cases possible are:
 ► 2, 3, 4, 6
So a total of 3 + 2 + 1 = 6 cases.
Hence, the correct answer is option D
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DIRECTIONSfor the question:Solve the following question and mark the b...
The Problem:
We are given that the only way to write 10 as the sum of 4 different natural numbers is 1, 2, 3, and 4. We need to determine how many different ways we can write 15 as the sum of 4 different natural numbers.

Approach:
To solve this problem, we can use a systematic approach by considering all possible combinations of natural numbers that add up to 15. We can start by listing down all the possible numbers that can be used in the sum.

Possible Numbers:
Since we need to write 15 as the sum of 4 different natural numbers, we can start by considering the smallest possible number which is 1. The other numbers can be determined by considering the difference between the desired sum (15) and the sum of the previous numbers.

Listing Possible Combinations:
Let's list down all the possible combinations of natural numbers that add up to 15:

1 + 2 + 3 + 9 = 15
1 + 2 + 4 + 8 = 15
1 + 2 + 5 + 7 = 15
1 + 2 + 6 + 6 = 15
1 + 3 + 4 + 7 = 15
1 + 3 + 5 + 6 = 15
1 + 4 + 5 + 5 = 15
2 + 3 + 4 + 6 = 15
2 + 3 + 5 + 5 = 15
2 + 4 + 4 + 5 = 15
3 + 4 + 4 + 4 = 15

Counting the Combinations:
From the above list, we can see that there are 11 different combinations of natural numbers that add up to 15. Therefore, the correct answer is option 'D' (None of these).

Conclusion:
In this problem, we used a systematic approach to determine all the possible combinations of natural numbers that add up to 15. By considering the smallest possible number and finding the difference between the desired sum and the sum of the previous numbers, we were able to list down all the combinations. Counting these combinations, we found that there are 11 different ways to write 15 as the sum of 4 different natural numbers.
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Directions: Read the following information carefully and answer the question that follows.Eleven books are written by different authors, named, O, D, Z, A, l, E, J, K, B, L and P. Their books are kept on different shelves. The bottom shelf is numbered 1 and the top one is numbered 11. The book written by B is kept on the third shelf. Two books are kept between the books written by O and A. There are as many books between the books written by O and A as those between the books written by P and K. The books written by O and P are on the top and the bottom shelf, respectively. The book written by L is on the seventh shelf. The book written by P is not kept above A. The book written by E is in the middle. The book written by J is kept between the books written by E and K. The book written by I is not kept on the shelf that is numbered above 8.Which author's book is kept on the tenth shelf?

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DIRECTIONSfor the question:Solve the following question and mark the best possible option.Q. The only way that 10 can be written as the sum of 4 different natural numbers is 1 + 2 + 3 + 4. In how many different ways can 15 be written as the sum of 4 different natural numbers?a)3b)4c)5d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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