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03 Aug 2022, 03:30
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B
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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
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03 Aug 2022, 09:59
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Bunuel
---ASIDE---------------
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
-----------------------
When a positive integer x is divided by 91, the remainder is 49
So, the smallest possible value of x is 49
What is the remainder when 2x is divided by 13 ?
Plug in our x-value to get: What is the remainder when 2(49) is divided by 13 ?
Simplify to get: What is the remainder when 98 is divided by 13 ?
98 divided by 13 equals 7 with remainder 7
Answer: B
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10 Sep 2022, 13:14
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We can express x in the form of pq + r, in which p is the divisor , q is the quotient and r is the remainder.
x = 91q + 49
2x = (91*2)q + 98
2x = (91*2)q + 91 + 7
The remainder when 2x is divided by is the sum of individual remainder.
Option B
x = 91q + 49
2x = (91*2)q + 98
2x = (91*2)q + 91 + 7
The remainder when 2x is divided by is the sum of individual remainder.
Option B
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