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What largest number will divide 47, 35 and 27 leaving same remainder in each case? What will be the common remainder?
- a)9,1
- b)1,9
- c)4,3
- d)3,4
- e)4,9
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What largest number will divide 47, 35 and 27 leaving same remainder i...
What to do when we don't lcnow the remainder and the largest number which divides?
In such cases subtract the 3 numbers from each other
47-35 = 12
35-27 = 8
27-47 = -20 (Ignore minus sign)
Largest number is needed that means we need HCF of 12, 8 and 20
In such cases subtract the 3 numbers from each other
47-35 = 12
35-27 = 8
27-47 = -20 (Ignore minus sign)
Largest number is needed that means we need HCF of 12, 8 and 20
Most Upvoted Answer
What largest number will divide 47, 35 and 27 leaving same remainder i...
Solution:
Let the common remainder be ‘x’. Then:
47 - x = 35 - x = 27 - x = k (some constant)
Therefore, 47 = k + x, 35 = k + x and 27 = k + x.
Using the above equations, we can find the value of k and x.
Calculating k and x:
k + x = 47
k + x = 35
k + x = 27
Subtracting the second equation from the first, we get:
12 = 0, which is not possible.
Therefore, there is no solution where the largest number will divide 47, 35 and 27 leaving the same remainder in each case.
Alternate Solution:
We can find the GCD (Greatest Common Divisor) of the differences of these numbers. That is:
GCD(47 - 35, 35 - 27, 47 - 27) = GCD(12, 8, 20) = 4
Therefore, the largest number that will divide 47, 35 and 27 leaving the same remainder in each case is 4.
Finding the common remainder:
Now, we need to find the common remainder ‘x’. We know that:
47 - x = 35 - x = 27 - x = k (some constant)
Substituting the value of k as 4, we get:
47 - x = 4
35 - x = 4
27 - x = 4
Solving for ‘x’ in each equation, we get:
x = 43
x = 31
x = 23
Therefore, the common remainder is 4 mod 23, 4 mod 31 and 4 mod 43, which is equal to 3.
Hence, the correct answer is option C) 4,3.
Let the common remainder be ‘x’. Then:
47 - x = 35 - x = 27 - x = k (some constant)
Therefore, 47 = k + x, 35 = k + x and 27 = k + x.
Using the above equations, we can find the value of k and x.
Calculating k and x:
k + x = 47
k + x = 35
k + x = 27
Subtracting the second equation from the first, we get:
12 = 0, which is not possible.
Therefore, there is no solution where the largest number will divide 47, 35 and 27 leaving the same remainder in each case.
Alternate Solution:
We can find the GCD (Greatest Common Divisor) of the differences of these numbers. That is:
GCD(47 - 35, 35 - 27, 47 - 27) = GCD(12, 8, 20) = 4
Therefore, the largest number that will divide 47, 35 and 27 leaving the same remainder in each case is 4.
Finding the common remainder:
Now, we need to find the common remainder ‘x’. We know that:
47 - x = 35 - x = 27 - x = k (some constant)
Substituting the value of k as 4, we get:
47 - x = 4
35 - x = 4
27 - x = 4
Solving for ‘x’ in each equation, we get:
x = 43
x = 31
x = 23
Therefore, the common remainder is 4 mod 23, 4 mod 31 and 4 mod 43, which is equal to 3.
Hence, the correct answer is option C) 4,3.
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What largest number will divide 47, 35 and 27 leaving same remainder in each case? What will be the common remainder?a)9,1b)1,9c)4,3d)3,4e)4,9Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What largest number will divide 47, 35 and 27 leaving same remainder in each case? What will be the common remainder?a)9,1b)1,9c)4,3d)3,4e)4,9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What largest number will divide 47, 35 and 27 leaving same remainder in each case? What will be the common remainder?a)9,1b)1,9c)4,3d)3,4e)4,9Correct answer is option 'C'. Can you explain this answer?.
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