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16 Jul 2023, 05:32
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B
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Difficulty:
35%
(medium)
Question Stats:
75% (01:48) correct
25%
(02:26)
wrong
based on 168
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When the positive integers m and n are divided by the positive integer d, they yield remainders of 17 and 27, respectively. If m + n, when divided by d, results in a remainder of 7, what is the value of d?
A. 34
B. 37
C. 44
D. 47
E. 51
M40-05
A. 34
B. 37
C. 44
D. 47
E. 51
M40-05
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07 Nov 2023, 09:56
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When the positive integers \(m\) and \(n\) are divided by the positive integer \(d\), they yield remainders of 17 and 27, respectively. If \(m + n\), when divided by \(d\), results in a remainder of 7, what is the value of \(d\)?
A. 34
B. 37
C. 44
D. 47
E. 51
The information given in the problem can be expressed as follows:
\(m = dq + 17\), where \(d > 17\).
\(n = dp + 27\), where \(d > 27\).
Adding these equations gives:
\(m + n = d(q+p) + 44\).
Given that \(m + n\), when divided by \(d\), yields a remainder of 7, we can rewrite the equation as:
\(m + n = d(q+p) + 37 + 7\).
This implies that \(d\) must be a factor of 37, and since \(d > 27\), the value of \(d\) must be 37.
Answer: B
A. 34
B. 37
C. 44
D. 47
E. 51
The information given in the problem can be expressed as follows:
\(m = dq + 17\), where \(d > 17\).
\(n = dp + 27\), where \(d > 27\).
Adding these equations gives:
\(m + n = d(q+p) + 44\).
Given that \(m + n\), when divided by \(d\), yields a remainder of 7, we can rewrite the equation as:
\(m + n = d(q+p) + 37 + 7\).
This implies that \(d\) must be a factor of 37, and since \(d > 27\), the value of \(d\) must be 37.
Answer: B
General Discussion
16 Jul 2023, 07:43
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Bunuel
\(m = d*q_1 + 17\) ; \(q_1\) → quotient when m is divided by d. Also, we can infer that \(0 < 17 < d\)
\(n = d*q_2 + 27\) ; \(q_2\) → quotient when n is divided by d. Also, we can infer that \(0 < 27 < d\)
\(m + n = d*(q_1+q_2) + 17 + 27\)
\(m + n = d*(q_1+q_2) + 44\)
\(m + n = d*(q_1+q_2) + 37 + 7\)
We know that \(d*(q_1+q_2)\) is divisible by d. It's also given that m + n, when divided by d, results in a remainder of 7. Hence 37 should be divisible by d.
Therefore d = 37.
Option B
