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07 Nov 2023, 02:50
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When a positive integer \(x\) is divided by 91, the remainder is 49. What is the remainder when \(2x\) is divided by 13 ?
A. 0
B. 7
C. 10
D. 12
E. 49
A. 0
B. 7
C. 10
D. 12
E. 49
07 Nov 2023, 02:50
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Official Solution:
When a positive integer \(x\) is divided by 91, the remainder is 49. What is the remainder when \(2x\) is divided by 13 ?
A. 0
B. 7
C. 10
D. 12
E. 49
\(x\) divided by 91, yielding a remainder of 49, can be expressed as \(x = 91q + 49\). Multiplying by 2 gives: \(2x = 2*91q + 98\). This can be rewritten as \(2x = 13*(14q + 7) + 7\). The first term, \(13*(14q + 7)\), is divisible by 13, and the last term, 7, when divided by 13, gives a remainder of 7.
Alternatively, we can reason as follows: Since a PS question can have only one correct answer, then considering one particular case which satisfies the conditions given must also yield the correct answer. If \(x\) divided by 91 yields a remainder of 49, then \(x\) can be 49. In this case, \(2x=98\), and 98 divided by 13 leaves a remainder of 7: \(98 = 13*7 + 7\).
Answer: B
When a positive integer \(x\) is divided by 91, the remainder is 49. What is the remainder when \(2x\) is divided by 13 ?
A. 0
B. 7
C. 10
D. 12
E. 49
\(x\) divided by 91, yielding a remainder of 49, can be expressed as \(x = 91q + 49\). Multiplying by 2 gives: \(2x = 2*91q + 98\). This can be rewritten as \(2x = 13*(14q + 7) + 7\). The first term, \(13*(14q + 7)\), is divisible by 13, and the last term, 7, when divided by 13, gives a remainder of 7.
Alternatively, we can reason as follows: Since a PS question can have only one correct answer, then considering one particular case which satisfies the conditions given must also yield the correct answer. If \(x\) divided by 91 yields a remainder of 49, then \(x\) can be 49. In this case, \(2x=98\), and 98 divided by 13 leaves a remainder of 7: \(98 = 13*7 + 7\).
Answer: B
24 May 2024, 00:08
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. 2x=13∗(14q+7)+7
I understand (14q +7), but where did the last +7 the one outside the bracket come from
I understand (14q +7), but where did the last +7 the one outside the bracket come from
