Latest Others Aptitude Question SOLUTION: Five consecutive positive integers have the property that the sum of the second, third and fourth is a perfect square, while the sum of all five is a perfect cube. If m is the thi

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(#M40019311) OTHERS Numerical Ability question Keep an EYE

Five consecutive positive integers have the property that the sum of the second, third and fourth is a perfect square, while the sum of all five is a perfect cube. If m is the third of these five integers, then the minimum possible value of m satisfies

(A) m ≤ 200
(B) 200 < m ≤ 400
(C) 400 < m ≤ 600
(D) 600 < m ≤ 800
(E) m > 800

Asked In Others mohan lal garg (10 years ago)

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Sameer Jain  (7 years ago)

We know that m being the third term (Middle term) is the 'mean or average' of these 5 consecutive integers so we can say-
Sum of 5 integers= 5*third term
--> Sum= 5m which ATQ is a perfect cube

Similarly, Sum=3m is a perfect square

So minimum possible value of m that satisfies both the conditions will be Cube of 3 x Square of 5 = 27x25= 675. Therefore D is the right option.

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