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When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3n
II. 5n
III. 4n + 10
II. 5n
III. 4n + 10
- a)I Only
- b)II Only
- c)III Only
- d)I & II Only
- e)I, II & III
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
When integer n is divided by 15, the remainder is 5. Which of the foll...
Understanding the Problem
When integer n is divided by 15, it leaves a remainder of 5. This can be expressed mathematically as:
n = 15k + 5, where k is an integer.
Now, we need to analyze the expressions to determine which ones leave a remainder of 10 when divided by 15.
Evaluating Each Expression
I. 3n
- Substitute n:
3n = 3(15k + 5) = 45k + 15.
- When divided by 15, the remainder is 0 (since 45k and 15 are both multiples of 15).
- Remainder: 0
II. 5n
- Substitute n:
5n = 5(15k + 5) = 75k + 25.
- When divided by 15:
75k is a multiple of 15 (remainder 0) and 25 divided by 15 leaves a remainder of 10.
- Remainder: 10
III. 4n + 10
- Substitute n:
4n + 10 = 4(15k + 5) + 10 = 60k + 20 + 10 = 60k + 30.
- When divided by 15, 60k is a multiple of 15 and 30 also leaves a remainder of 0.
- Remainder: 0
Conclusion
- Expressions I and III do not satisfy the condition of leaving a remainder of 10 when divided by 15.
- Only Expression II (5n) meets the requirement.
Thus, the correct answer is option 'B' (II Only).
When integer n is divided by 15, it leaves a remainder of 5. This can be expressed mathematically as:
n = 15k + 5, where k is an integer.
Now, we need to analyze the expressions to determine which ones leave a remainder of 10 when divided by 15.
Evaluating Each Expression
I. 3n
- Substitute n:
3n = 3(15k + 5) = 45k + 15.
- When divided by 15, the remainder is 0 (since 45k and 15 are both multiples of 15).
- Remainder: 0
II. 5n
- Substitute n:
5n = 5(15k + 5) = 75k + 25.
- When divided by 15:
75k is a multiple of 15 (remainder 0) and 25 divided by 15 leaves a remainder of 10.
- Remainder: 10
III. 4n + 10
- Substitute n:
4n + 10 = 4(15k + 5) + 10 = 60k + 20 + 10 = 60k + 30.
- When divided by 15, 60k is a multiple of 15 and 30 also leaves a remainder of 0.
- Remainder: 0
Conclusion
- Expressions I and III do not satisfy the condition of leaving a remainder of 10 when divided by 15.
- Only Expression II (5n) meets the requirement.
Thus, the correct answer is option 'B' (II Only).
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When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?I. 3nII. 5nIII. 4n + 10a)I Onlyb)II Onlyc)III Onlyd)I & II Onlye)I, II & IIICorrect answer is option 'B'. Can you explain this answer?
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When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?I. 3nII. 5nIII. 4n + 10a)I Onlyb)II Onlyc)III Onlyd)I & II Onlye)I, II & IIICorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?I. 3nII. 5nIII. 4n + 10a)I Onlyb)II Onlyc)III Onlyd)I & II Onlye)I, II & IIICorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?I. 3nII. 5nIII. 4n + 10a)I Onlyb)II Onlyc)III Onlyd)I & II Onlye)I, II & IIICorrect answer is option 'B'. Can you explain this answer?.
When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?I. 3nII. 5nIII. 4n + 10a)I Onlyb)II Onlyc)III Onlyd)I & II Onlye)I, II & IIICorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?I. 3nII. 5nIII. 4n + 10a)I Onlyb)II Onlyc)III Onlyd)I & II Onlye)I, II & IIICorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?I. 3nII. 5nIII. 4n + 10a)I Onlyb)II Onlyc)III Onlyd)I & II Onlye)I, II & IIICorrect answer is option 'B'. Can you explain this answer?.
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