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A number x when divided by 289 leaves 18 as the remainder. The same number when divided by 17 leaves y as a remainder. The value of y is (SSC CGL 2nd Sit. 2013)
- a)3
- b)1
- c)5
- d)2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A number x when divided by 289 leaves 18 as the remainder. The same nu...
Here, the first divisor (289) is a multiple of second divisor (17).
∴ Required remainder = Remainder obtained on dividing 18 by 17 = 1
∴ Required remainder = Remainder obtained on dividing 18 by 17 = 1
Most Upvoted Answer
A number x when divided by 289 leaves 18 as the remainder. The same nu...
To find the value of y, we can use the concept of congruence.
Let's assume the number x to be a.
According to the given information,
a divided by 289 leaves 18 as the remainder.
This can be written as: a ≡ 18 (mod 289)
Also, a divided by 17 leaves y as the remainder.
This can be written as: a ≡ y (mod 17)
Now, we can solve these congruences simultaneously to find the value of y.
**Solving the first congruence:**
a ≡ 18 (mod 289)
To solve this congruence, we need to find the value of a that satisfies the given condition.
Let's express a as:
a = 289k + 18, where k is an integer.
By substituting the value of a in the congruence, we get:
289k + 18 ≡ 18 (mod 289)
Subtracting 18 from both sides, we have:
289k ≡ 0 (mod 289)
Dividing both sides by 289, we get:
k ≡ 0 (mod 1)
Since k can take any value, we can say that a ≡ 18 (mod 289) for all values of a.
**Solving the second congruence:**
a ≡ y (mod 17)
Similarly, let's express a as:
a = 17m + y, where m is an integer.
By substituting the value of a in the congruence, we get:
17m + y ≡ y (mod 17)
Subtracting y from both sides, we have:
17m ≡ 0 (mod 17)
Dividing both sides by 17, we get:
m ≡ 0 (mod 1)
Since m can take any value, we can say that a ≡ y (mod 17) for all values of a.
Therefore, the value of y can be any integer, and it is not uniquely determined by the given information.
Hence, the correct answer is option 'B' (1).
Let's assume the number x to be a.
According to the given information,
a divided by 289 leaves 18 as the remainder.
This can be written as: a ≡ 18 (mod 289)
Also, a divided by 17 leaves y as the remainder.
This can be written as: a ≡ y (mod 17)
Now, we can solve these congruences simultaneously to find the value of y.
**Solving the first congruence:**
a ≡ 18 (mod 289)
To solve this congruence, we need to find the value of a that satisfies the given condition.
Let's express a as:
a = 289k + 18, where k is an integer.
By substituting the value of a in the congruence, we get:
289k + 18 ≡ 18 (mod 289)
Subtracting 18 from both sides, we have:
289k ≡ 0 (mod 289)
Dividing both sides by 289, we get:
k ≡ 0 (mod 1)
Since k can take any value, we can say that a ≡ 18 (mod 289) for all values of a.
**Solving the second congruence:**
a ≡ y (mod 17)
Similarly, let's express a as:
a = 17m + y, where m is an integer.
By substituting the value of a in the congruence, we get:
17m + y ≡ y (mod 17)
Subtracting y from both sides, we have:
17m ≡ 0 (mod 17)
Dividing both sides by 17, we get:
m ≡ 0 (mod 1)
Since m can take any value, we can say that a ≡ y (mod 17) for all values of a.
Therefore, the value of y can be any integer, and it is not uniquely determined by the given information.
Hence, the correct answer is option 'B' (1).
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A number x when divided by 289 leaves 18 as the remainder. The same number when divided by 17 leaves y as a remainder. The value of y is (SSC CGL 2nd Sit. 2013)a)3b)1c)5d)2Correct answer is option 'B'. Can you explain this answer?
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