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Difficulty:
65%
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Question Stats:
61% (02:19) correct
39%
(02:20)
wrong
based on 324
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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
_________________
(A) 37
(B) 39
(C) 41
(D) 43
(E) 45
_________________
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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)
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)
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
_________________
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
_________________
How to Solve :
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
General Discussion
ashishpathak
Joined: 01 Jul 2021
Last visit: 07 Feb 2025
Posts: 28
Location: India
Schools: ISB '25 (A)
GMAT 1: 620 Q42 V34
GMAT 2: 650 Q46 V34
GPA: 2.57
WE:Military Officer (Aerospace and Defense)
what should be the approach to solve this question? other than dividing each individually.
Posts: 4
Solenja
Hello Expert,
What is the reason or logic behind subtracting the numbers 3962, 4085 and 4167 among themselves ?
Posts: 1,070
shivamagarwal
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?
Posts: 1,382
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
Bunuel
GMAT Focus 1: 675 Q85 V86 DI79
Posts: 4
Beautiful solution
Solenja
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