When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?
A. 5
B. 7
C. 11
D. 14
E. 21
OA B
Source: Veritas Prep
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When positive integer k is divided by 35, the remainder is
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BTGmoderatorDC
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Jay@ManhattanReview
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Say when the positive integer k is divided by 35, the quotient is q and the remainder is 14. Then, we haveBTGmoderatorDC wrote:When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?
A. 5
B. 7
C. 11
D. 14
E. 21
OA B
Source: Veritas Prep
k = 35q + 14
k = 7(5k + 2)
We see that k must be a multiple of 7 or divisible by 7.
The correct answer: B
Hope this helps!
-Jay
The correct answer: [spoiler][/spoiler]
Hope this helps!
-Jay
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\(K = 35Q+14\)
When \(Q = 1\)
\(K = 49 \cdots \) it is divisible by \(7\)
When \(Q = 2\)
\(K = 84 \cdots\) it is divisible by \(7\) and \(21\)
When \(Q = 3\)
\(K = 109\).
it is divisible by \(7 \cdots \)
Therefore, __B__ is the correct answer.
When \(Q = 1\)
\(K = 49 \cdots \) it is divisible by \(7\)
When \(Q = 2\)
\(K = 84 \cdots\) it is divisible by \(7\) and \(21\)
When \(Q = 3\)
\(K = 109\).
it is divisible by \(7 \cdots \)
Therefore, __B__ is the correct answer.
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Scott@TargetTestPrep
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BTGmoderatorDC wrote:When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?
A. 5
B. 7
C. 11
D. 14
E. 21
OA B
Source: Veritas Prep
We can create the following equation:
k = 35Q + 14
We see that 35Q + 14 is divisible by 7.
Answer: B
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