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Two different numbers when divided by same divisor leaves remainder 7 and 9 respectively. When their sum is divided by the same divisor remainder was 4. Find the divisor?
- a)11
- b)12
- c)13
- d)14
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two different numbers when divided by same divisor leaves remainder 7 ...
Let first number N1 = D*a + 7
and second number N2 = D*b + 9
N1 + N2 = (a+b)*D + 16
Remainder is 4, so D will be 12
and second number N2 = D*b + 9
N1 + N2 = (a+b)*D + 16
Remainder is 4, so D will be 12
Most Upvoted Answer
Two different numbers when divided by same divisor leaves remainder 7 ...
Given: Two different numbers leave remainders of 7 and 9 respectively when divided by a certain divisor. When their sum is divided by the same divisor, the remainder is 4.
To find: The divisor.
Solution:
Let the two different numbers be a and b.
a ÷ d = p1 (quotient) and leaves a remainder of 7
b ÷ d = p2 (quotient) and leaves a remainder of 9
So, a = d × p1 + 7 and b = d × p2 + 9
When (a + b) is divided by d, the remainder is 4.
(a + b) ÷ d = p3 (quotient) and leaves a remainder of 4
Substituting the values of a and b in the above equation, we get,
(d × p1 + 7) + (d × p2 + 9) ÷ d = p3 and leaves a remainder of 4
⇒ d(p1 + p2) + 16 ÷ d = p3 and leaves a remainder of 4
⇒ d(p1 + p2) ÷ d + 16 ÷ d = p3 and leaves a remainder of 4
⇒ p1 + p2 + 16 ÷ d = p3 and leaves a remainder of 4
⇒ p1 + p2 = p3 + 4/ d
We know that p1, p2, and p3 are integers, and p1 + p2 is also an integer.
This means that 4/ d must also be an integer, which is possible only when d = 2 × 2 × 3 = 12.
Therefore, the divisor is 12.
Hence, option (b) is the correct answer.
To find: The divisor.
Solution:
Let the two different numbers be a and b.
a ÷ d = p1 (quotient) and leaves a remainder of 7
b ÷ d = p2 (quotient) and leaves a remainder of 9
So, a = d × p1 + 7 and b = d × p2 + 9
When (a + b) is divided by d, the remainder is 4.
(a + b) ÷ d = p3 (quotient) and leaves a remainder of 4
Substituting the values of a and b in the above equation, we get,
(d × p1 + 7) + (d × p2 + 9) ÷ d = p3 and leaves a remainder of 4
⇒ d(p1 + p2) + 16 ÷ d = p3 and leaves a remainder of 4
⇒ d(p1 + p2) ÷ d + 16 ÷ d = p3 and leaves a remainder of 4
⇒ p1 + p2 + 16 ÷ d = p3 and leaves a remainder of 4
⇒ p1 + p2 = p3 + 4/ d
We know that p1, p2, and p3 are integers, and p1 + p2 is also an integer.
This means that 4/ d must also be an integer, which is possible only when d = 2 × 2 × 3 = 12.
Therefore, the divisor is 12.
Hence, option (b) is the correct answer.
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Two different numbers when divided by same divisor leaves remainder 7 and 9 respectively. When their sum is divided by the same divisor remainder was 4. Find the divisor?a)11b)12c)13d)14e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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