What is the greatest positive integer which will divide 3962, 4085 and

Question

What is the greatest positive integer which will divide 3962, 4085 and 4167 leaving the same remainder in each case?

(A) 37
(B) 39
(C) 41
(D) 43
(E) 45

Solenja · Accepted Answer

Explanation:

We have to find Greatest Factor

In this case , we have to find HCF with remainder

Step 1: Find the Differences of numbers

Step 2: Get the HCF ( that differences)

We have here 3962, 4085 and 4167

So differences are

4167 - 4085 = 82

4167 - 3962 = 205,

4085 - 3962 = 123.

Now

HCF (82, 123 and 205)

As

82 = 2 x 41

123 = 3 x 41

205 = 5 x 41

HCF = 41.

And 41 is the required number.(source:internet)

ashishpathak · Answer

what should be the approach to solve this question? other than dividing each individually.

shivamagarwal · Answer

Hello Expert,

What is the reason or logic behind subtracting the numbers 3962, 4085 and 4167 among themselves ?

ThatDudeKnows · Answer

shivamagarwal

In order be left with the same remainder, we must add one or more "steps" between each of the numbers in the question stem such that the size of the steps are all the same. The  number  of steps from the first number to the second need not equal the number of steps from the second number to the third, but the  size  of each step must be the same. In this case, the distance between 3962 and 4085 is 123 and the distance between 4085 and 4167 is 82. We can therefore take three steps of size 41 to get from 3962 to 4085 and two steps of size 41 to get from 4085 to 4167. Do that help you wrap your head around it?

BrushMyQuant · Answer

What is the greatest positive integer which will divide 3962, 4085 and 4167 leaving the same remainder in each case?

Dividend = Divisor * Quotient + Remainder

=> 3962 = x*a + r (where x is the divided, a is the quotient and r is the remainder)
 => 4085 = x*b + r (where x is the divided, b is the quotient and r is the remainder) 
 => 4167 = x*c + r (where x is the divided, c is the quotient and r is the remainder)

4167 - 3962  = xc + r - (xa + r) = xc - xa = x*(c-a)
=> 205 = x*(c-a)
=> x must divided a factor of 205

4167 - 4085  = xc + r - (xb + r) = xc - xb = x*(c-b)
=> 82 = x*(c-b)
=> x must divided a factor of 91

4085 - 3962  = xb + r - (xa + r) = xb - xa = x*(b-a)
=> 123 = x*(b-a)
=> x must divided a factor of 123

=>  x must be a factor of GCD(82,123,205) 
82 = 41 * 2
123 = 41 * 3
205 = 41 * 5
=> GCD(82,123,205) = 41

Watch  this video  to MASTER LCM and GCD ]

So,  Answer will be C 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

ManifestDreamMBA · Answer

Given the answer choices are co-prime, I will pick the difference b/w closest integers. 4167-4085 = 82 which is 41*2. Answer is 41

bumpbot · Answer

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What is the greatest positive integer which will divide 3962, 4085 and

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What is the greatest positive integer which will divide 3962, 4085 and

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