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The remainder when the positive integer m is divided by n is r. What is the remainder when 2m is divided by 2n?
- a)r
- b)2r
- c)2n
- d)m - nr
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The remainder when the positive integer m is divided by n is r. What i...
Plug in some numebrs and check - m = 5 n = 3 r = 2 What is the remainder when 2m is divided by 2n ? 2m = 10 2n = 6 So, Remainder when 2m is divided by 2n is = 4 2r = 4 Thus, answer must be 2r
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Most Upvoted Answer
The remainder when the positive integer m is divided by n is r. What i...
Solution:
Let's assume that m = qn + r, where q is a quotient and r is the remainder when m is divided by n.
We need to find the remainder when 2m is divided by 2n.
Let's first simplify 2m:
2m = 2(qn + r)
= 2qn + 2r
= 2(qn) + r + r
= n(2q) + r + r
= n(2q) + 2r
Now, let's divide 2m by 2n:
2m ÷ 2n = (n(2q) + 2r) ÷ 2n
= nq + r
Therefore, the remainder when 2m is divided by 2n is r + r = 2r.
Hence, the correct answer is option B.
Let's assume that m = qn + r, where q is a quotient and r is the remainder when m is divided by n.
We need to find the remainder when 2m is divided by 2n.
Let's first simplify 2m:
2m = 2(qn + r)
= 2qn + 2r
= 2(qn) + r + r
= n(2q) + r + r
= n(2q) + 2r
Now, let's divide 2m by 2n:
2m ÷ 2n = (n(2q) + 2r) ÷ 2n
= nq + r
Therefore, the remainder when 2m is divided by 2n is r + r = 2r.
Hence, the correct answer is option B.
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