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For the positive integers k, m and n, k(m)n means that the remainder when m is divided by n is k. If k(13766)9 and p(137)k, where p is a positive integer, then p is equal to.
- a)1
- b)2
- c)5
- d)7
- e)8
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
For the positive integers k, m and n, k(m)n means that the remainder w...
Given:
- For positive integers k, m and n, k(m)n implies k is the remainder when m is divided by n
- k(13766)9 → k is the remainder when 13766 is divided by 9
- p(137)k → p is the remainder when 137 is divided by k
- p is a positive integer
To find: p = ?
Approach:
- To find the value of p, we need to evaluate the expression p(137)k
- However, this expression also contains k
- So, we’ll be able to find the value of p only when we first know the value of k
- We can find the value of k by evaluating the expression k(13766)9
Working Out:
- Finding the value of k
- k(13766)9 means that the remainder when 13766 is divided by 9 is k.
- Sum of digits of 13766 = 1+3+7+6+6 = 23
- So, remainder when 13766 is divided with 9 = Remainder that 23 leaves with 9 = 5
- Thus, k = 5
- Finding the value of p
- p(137)k means that the remainder when 137 is divided by k is p
- We’ve inferred above that k = 5
- So, the above expression means that when 137 is divided by 5, the remainder is p
- Now, 137 leaves a remainder of 2 with 5
- So, p= 2
- p(137)k means that the remainder when 137 is divided by k is p
Looking at the answer choices, we see that the correct answer is Option B
Most Upvoted Answer
For the positive integers k, m and n, k(m)n means that the remainder w...
To solve this problem, we need to understand the properties of the operation k(m)n and use them to find the value of p in p(137)k.
Understanding the operation k(m)n:
- In the operation k(m)n, the remainder when m is divided by n is k.
- This means that k is the difference between m and the largest multiple of n that is less than or equal to m.
Solving k(13766)9:
- We are given that k(13766)9.
- This means that the remainder when 13766 is divided by 9 is k.
- To find k, we need to find the largest multiple of 9 that is less than or equal to 13766.
- The largest multiple of 9 less than or equal to 13766 is 13761 (9 * 1529).
- Therefore, k = 13766 - 13761 = 5.
Finding the value of p in p(137)k:
- We are given that p(137)k.
- This means that the remainder when 137 is divided by k is p.
- To find p, we need to find the largest multiple of k that is less than or equal to 137.
- Since k = 5, we need to find the largest multiple of 5 that is less than or equal to 137.
- The largest multiple of 5 less than or equal to 137 is 135 (5 * 27).
- Therefore, p = 137 - 135 = 2.
Conclusion:
- The value of p in p(137)k is 2.
- Therefore, the correct answer is option B.
Understanding the operation k(m)n:
- In the operation k(m)n, the remainder when m is divided by n is k.
- This means that k is the difference between m and the largest multiple of n that is less than or equal to m.
Solving k(13766)9:
- We are given that k(13766)9.
- This means that the remainder when 13766 is divided by 9 is k.
- To find k, we need to find the largest multiple of 9 that is less than or equal to 13766.
- The largest multiple of 9 less than or equal to 13766 is 13761 (9 * 1529).
- Therefore, k = 13766 - 13761 = 5.
Finding the value of p in p(137)k:
- We are given that p(137)k.
- This means that the remainder when 137 is divided by k is p.
- To find p, we need to find the largest multiple of k that is less than or equal to 137.
- Since k = 5, we need to find the largest multiple of 5 that is less than or equal to 137.
- The largest multiple of 5 less than or equal to 137 is 135 (5 * 27).
- Therefore, p = 137 - 135 = 2.
Conclusion:
- The value of p in p(137)k is 2.
- Therefore, the correct answer is option B.
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