Question 883921: if K, a positive two-digit integer, is divided by 13, a remainder of 6 results. When the same number is divided by 6 or 7, the remainder is 3. What is the value of K?
(A) 45
(B)58
(C)71
(D)84
(E)97
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Try out each answer choice
A)
45/13 = 3 remainder 6
45/6 = 7 remainder 3
45/7 = 6 remainder 3
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B)
58/13 = 4 remainder 6
58/6 = 9 remainder 4 <--- Remainder is NOT 3, so it can't be choice B
58/7 = 8 remainder 2 <--- Remainder is NOT 3, so it can't be choice B
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C)
71/13 = 5 remainder 6
71/6 = 11 remainder 5 <--- Remainder is NOT 3, so it can't be choice C
71/7 = 10 remainder 1 <--- Remainder is NOT 3, so it can't be choice C
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D)
84/13 = 6 remainder 6
84/6 = 14 remainder 0 <--- Remainder is NOT 3, so it can't be choice D
84/7 = 12 remainder 0 <--- Remainder is NOT 3, so it can't be choice D
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E)
97/13 = 7 remainder 6
97/6 = 16 remainder 1 <--- Remainder is NOT 3, so it can't be choice E
97/7 = 13 remainder 6 <--- Remainder is NOT 3, so it can't be choice E
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So the answer is (A) 45
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! if K, a positive two-digit integer, is divided by 13, a remainder of 6 results. When the same number is divided by 6 or 7, the remainder is 3. What is the value of K?
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y1 = (x-6)/13
y2 = (x-3)/6
y3 = (x-3)/7
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Find a value of "x" that gives integer values for y1, y2, y3::
x = 45
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(A) 45
(B)58
(C)71
(D)84
(E)97
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