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The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers. Which of the following must be true?
I. k = 2
II. r = 9
III. s = 5
I. k = 2
II. r = 9
III. s = 5
- a)I only
- b)II only
- c)III only
- d)I and II
- e)II and III
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The three-digit integer kss is the sum of the two-digit integers ks an...
Given Information:
The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers.
Analysis:
To determine which statements must be true, let's break down the problem:
- The three-digit integer kss is formed by k, s, and s.
- The two-digit integers ks and rs are formed by k and s, and r and s, respectively.
- The sum of ks and rs results in kss.
Explanation:
- Statement I: k = 2
If k = 2, then the hundreds place of kss is 2. However, since kss is a three-digit integer, k cannot be 2. Therefore, statement I is not true.
- Statement II: r = 9
If r = 9, then the tens place of rs is 9. This would make the sum of ks and rs greater than 100, which is not possible for a two-digit integer. Therefore, statement II is not true.
- Statement III: s = 5
If s = 5, then the units place of ks and rs is 5. When 5 is added to any two-digit number, the result will have 5 in the units place. Therefore, statement III must be true.
Conclusion:
Therefore, the only statement that must be true is III only.
Community Answer
The three-digit integer kss is the sum of the two-digit integers ks an...
The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers.
Since kss is a three-digit number, it implies that k cannot be zero.
Now, let's consider the possibilities for the two-digit integers ks and rs:
If both ks and rs have a tens digit of 1, the sum would result in a three-digit number with a thousands digit of 2 (k = 2).
If both ks and rs have a ones digit of 9, the sum would result in a three-digit number with a hundreds digit of 9 (r = 9).
If both ks and rs have a ones digit of 5, the sum would result in a three-digit number with a ones digit of 0 or 1, which is not possible.
Based on the analysis, we can conclude that option II (r = 9) must be true, as it is the only valid and necessary condition for the sum of the two-digit integers to result in a three-digit integer kss.
If both ks and rs have a ones digit of 9, the sum would result in a three-digit number with a hundreds digit of 9 (r = 9).
If both ks and rs have a ones digit of 5, the sum would result in a three-digit number with a ones digit of 0 or 1, which is not possible.
Based on the analysis, we can conclude that option II (r = 9) must be true, as it is the only valid and necessary condition for the sum of the two-digit integers to result in a three-digit integer kss.
Therefore, the correct answer is B: II only.
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The three-digit integer kss is the sum of the two-digit integers ks and rs, where k, r, and s are the digits of the integers. Which of the following must be true?I. k = 2II. r = 9III. s = 5a)I onlyb)II onlyc)III onlyd)I and IIe)II and IIICorrect answer is option 'B'. Can you explain this answer?
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