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From the longer of two rods a piece equal to the shorter is cut off: with the shorter and the remainder of the larger a similar operation is performed, and so on, until the rods are of equal length. If this last length be taken for the unit of measurement, the length of original rods will be represented by number which are:
(A) Both even
(B) Both odd
(C) One number is multiple of the other
(D) Prime to each other
(E) Both are multiples of 3
(A) Both even
(B) Both odd
(C) One number is multiple of the other
(D) Prime to each other
(E) Both are multiples of 3
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09 Sep 2026, 04:15
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assume rod lengths to be x and y, we have to find the greatest common divisor (HCF) of x and y.
let the final length = d so, d= gcd(x,y)
since we are asked to represent the original lengths as multiples of the new unit we can take this as- x/d and y/d
they will no remaining common factor other than 1 so they are coprime to each other.
eg- we assume 14 and 10 as the lengths:
1. subtract 10 from 14. new lengths= 4 and 10
2. subtract 4 from 10. new lengths= 4 and 6
3. subtract 4 from 6. new lengths= 4 and 2
4. subtract 2 from 4. new= 2 and 2
rods are now equal so final GCD is 2. using this we get original rods as 14/2 = 7 and 10/2 = 5
7 and 5 are prime to each other
let the final length = d so, d= gcd(x,y)
since we are asked to represent the original lengths as multiples of the new unit we can take this as- x/d and y/d
they will no remaining common factor other than 1 so they are coprime to each other.
eg- we assume 14 and 10 as the lengths:
1. subtract 10 from 14. new lengths= 4 and 10
2. subtract 4 from 10. new lengths= 4 and 6
3. subtract 4 from 6. new lengths= 4 and 2
4. subtract 2 from 4. new= 2 and 2
rods are now equal so final GCD is 2. using this we get original rods as 14/2 = 7 and 10/2 = 5
7 and 5 are prime to each other
Gmatiseasyforall
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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