Question 1190940
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Linda's age is twice her sister's age. 
Difference between their ages is a perfect square number. 
If the difference in their age is between 5 years and 40 years, 
what is the difference between the highest and the lowest possible values of Linda's age?
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Let x be the sister's age.

Then the Linda's age is 2x, according to the problem.



The difference of their ages  2x-x = x  is the perfect square number between 5 and 40.


So, x is one of the numbers 9, 16, 25, 36.


Thus the minimum Landa's age is 2*9 = 18 years, and the maximum Linda's age is 2*36 = 72 years.


The difference between the highest and the lowest possible values of Linda's age is 72 - 18 = 54 years.
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Solved.


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This problem is presented as a Math problem, so, my major concern is to make it logically consistent.


I do not go in discussing whether it is realistic to have a difference of ages of 36 years between the sisters.