Latest MBA Aptitude Question SOLUTION: Let Sm denote the sum of the squares of first m natural numbers. For How many values of m<100,is Sm a multiple of 4?

1) 50
2) 25
3) 36
4) 24

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(#M40016099) MBA question number systems, progressions Keep an EYE

Let Sm denote the sum of the squares of first m natural numbers. For How many values of m<100,is Sm a multiple of 4?

1) 50
2) 25
3) 36
4) 24

Asked In MBA (11 years ago)

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Mohammad Akram  (9 years ago)

24
Sm=(1^2 +2^2+....+m^2)=m(m+1)(2m+1)/6,
if the sum is divisible by 4 then ,we can say that " m(m+1)(2m+1)/24 " will be an integer.
from (1-10) => 7,8
(11-20)=>15,16
..........................
(91-99) => 95,96
so here we get an AP i.e.
7,8,15,16.......95.96. => 7,15,.... ,95 && 8,16, ...... , 96
number of terms in both series are,
12+12=24

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Chirag Ranjan Lahiri  (9 years ago)

its 24
Sm=(1^2 +2^2+....+m^2)=m(m+1)(2m+1)/6

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