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20 Jan 2024, 00:48
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I have this question: A number leaves remainder 2 when divided by 11. What remainder may it leaves when divided by 44?
A. 13
B. 39
C. 42
So my solution is:
Let's call that number is A
A = 11k+2
=> A is divided by 44 means that (11k+2)/44
Because 2/44 has remainder 2, so the remainder of (11k+2)/44 depends on the remainder of 11k/44
Then I try with various value of k from 1, 2, 3...
And I got that:
If k=1 -> the remainder is 11
If k=2 -> the remainder is 22
If k=3 -> the remainder is 33
if K =4 -> the remainder is 0
And this will be the same for k = 5,6,7...
So 11k/44 will have 3 remainders 11, 22, 33 with different k
Hence the answer is A
But I think it has another way to have the conclusion.
I mean, normally 11k/44 = B + r, with 11<r<44. But how can we know that r just can only 11, 22, and 33 without try with different k value
Really hope that I can get help from you guys
((
Thank you so much!!!
A. 13
B. 39
C. 42
So my solution is:
Let's call that number is A
A = 11k+2
=> A is divided by 44 means that (11k+2)/44
Because 2/44 has remainder 2, so the remainder of (11k+2)/44 depends on the remainder of 11k/44
Then I try with various value of k from 1, 2, 3...
And I got that:
If k=1 -> the remainder is 11
If k=2 -> the remainder is 22
If k=3 -> the remainder is 33
if K =4 -> the remainder is 0
And this will be the same for k = 5,6,7...
So 11k/44 will have 3 remainders 11, 22, 33 with different k
Hence the answer is A
But I think it has another way to have the conclusion.
I mean, normally 11k/44 = B + r, with 11<r<44. But how can we know that r just can only 11, 22, and 33 without try with different k value
Really hope that I can get help from you guys
((Thank you so much!!!
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20 Jan 2024, 01:52
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phuongdung0204
Please repost the question according to the rules: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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