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Ena's age was square of a number last year and it will be cube of a number next year. How long must at least she wait before her age be again the cube of a number?1. 10 years2. 20 years3. 38 years4. 42 years |
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Answer» Correct Answer - Option 3 : 38 years Calculation: Let Ena's age be 'x' Last year Ena's age is equal to the square of a number ⇒ x - 1 = n2 ----(1) After 1 year age is equal to the cube of the number ⇒ x + 1 = m3 ----(2) Last year and Next year are 2 years apart, so we have to find the square and cube with a difference of 2. Squares of numbers = 1, 4, 9, 16, 25, 36, 49, 64,..... Cubes of numbers = 1, 8, 27, 64, 125, 216,.... Add 2 in squares of numbers = 3, 6, 11, 18, 27, 38, 51, 66, .... We can notice 27 cubes only we are getting after adding 2 Current age of Ena's = 25 + 1 = 26 years 27 is the cube of 33 = 27 and next cube is 43 = 64 Ena's has to wait = 64 - 26 = 38 years ∴ Ena's has to wait 38 years. |
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