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When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
- a)339
- b)349
- c)369
- d)data inadequate
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
When a number is divided by 13, the remainder is 11. When the same num...
X= 13p + 11 and X= 17q + 9, Hence
13p + 11 = 17q + 9
17q - 13p = 2
q = (2 + 13p)/17
The least value for p for which q = (2 + 13p)/17 is a whole number is p = 26
Therefore x=(13*26 + 11) = (338 + 11) = 349
Most Upvoted Answer
When a number is divided by 13, the remainder is 11. When the same num...
To find the number, we can use the concept of congruence.
Let's assume the number we are trying to find is represented by 'x'.
Given:
x ≡ 11 (mod 13) --------(1)
x ≡ 9 (mod 17) --------(2)
We need to find a number that satisfies both congruences.
Using Congruence (1):
We know that when x is divided by 13, the remainder is 11.
This can be written as:
x = 13a + 11, where 'a' is an integer.
Using Congruence (2):
We know that when x is divided by 17, the remainder is 9.
This can be written as:
x = 17b + 9, where 'b' is an integer.
Solving both equations:
Since x is the same in both equations, we can equate the two expressions for x:
13a + 11 = 17b + 9
Simplifying the equation:
13a - 17b = -2
To find the values of 'a' and 'b', we can try substituting different values for 'a' and find a corresponding value for 'b'. We can start with 'a = 1', and solve for 'b'.
13(1) - 17b = -2
13 - 17b = -2
17b = 15
b = 15/17 (which is not an integer)
Trying Again:
Let's try with 'a = 2'
13(2) - 17b = -2
26 - 17b = -2
17b = 28
b = 28/17 (which is not an integer)
Trying Again:
Let's try with 'a = 3'
13(3) - 17b = -2
39 - 17b = -2
17b = 41
b = 41/17 (which is not an integer)
Trying Again:
Let's try with 'a = 4'
13(4) - 17b = -2
52 - 17b = -2
17b = 54
b = 54/17 (which is not an integer)
Trying Again:
Let's try with 'a = 5'
13(5) - 17b = -2
65 - 17b = -2
17b = 67
b = 67/17 (which is not an integer)
Trying Again:
Let's try with 'a = 6'
13(6) - 17b = -2
78 - 17b = -2
17b = 80
b = 80/17 (which is not an integer)
Trying Again:
Let's try with 'a = 7'
13(7) - 17b = -2
91 - 17b = -2
17b = 93
b = 93/17 (which is not an integer)
Trying Again:
Let's try with 'a = 8'
13(8) - 17b = -2
104 - 17
Let's assume the number we are trying to find is represented by 'x'.
Given:
x ≡ 11 (mod 13) --------(1)
x ≡ 9 (mod 17) --------(2)
We need to find a number that satisfies both congruences.
Using Congruence (1):
We know that when x is divided by 13, the remainder is 11.
This can be written as:
x = 13a + 11, where 'a' is an integer.
Using Congruence (2):
We know that when x is divided by 17, the remainder is 9.
This can be written as:
x = 17b + 9, where 'b' is an integer.
Solving both equations:
Since x is the same in both equations, we can equate the two expressions for x:
13a + 11 = 17b + 9
Simplifying the equation:
13a - 17b = -2
To find the values of 'a' and 'b', we can try substituting different values for 'a' and find a corresponding value for 'b'. We can start with 'a = 1', and solve for 'b'.
13(1) - 17b = -2
13 - 17b = -2
17b = 15
b = 15/17 (which is not an integer)
Trying Again:
Let's try with 'a = 2'
13(2) - 17b = -2
26 - 17b = -2
17b = 28
b = 28/17 (which is not an integer)
Trying Again:
Let's try with 'a = 3'
13(3) - 17b = -2
39 - 17b = -2
17b = 41
b = 41/17 (which is not an integer)
Trying Again:
Let's try with 'a = 4'
13(4) - 17b = -2
52 - 17b = -2
17b = 54
b = 54/17 (which is not an integer)
Trying Again:
Let's try with 'a = 5'
13(5) - 17b = -2
65 - 17b = -2
17b = 67
b = 67/17 (which is not an integer)
Trying Again:
Let's try with 'a = 6'
13(6) - 17b = -2
78 - 17b = -2
17b = 80
b = 80/17 (which is not an integer)
Trying Again:
Let's try with 'a = 7'
13(7) - 17b = -2
91 - 17b = -2
17b = 93
b = 93/17 (which is not an integer)
Trying Again:
Let's try with 'a = 8'
13(8) - 17b = -2
104 - 17
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When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?a)339b)349c)369d)data inadequateCorrect answer is option 'B'. Can you explain this answer?
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