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If the product of three consecutive positive integers is 15600 then

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If the product of three consecutive positive integers is 15600 then  [#permalink]

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New post 07 Sep 2018, 00:31
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If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

A) 1777
B) 1785
C) 1875
D) 1877
E) 1897

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Re: If the product of three consecutive positive integers is 15600 then  [#permalink]

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New post 07 Sep 2018, 04:33
AkshdeepS wrote:
If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

A) 1777
B) 1785
C) 1875
D) 1877
E) 1897



\(15600=2*2*3*13*2*5*2*5\)
A immediate though should no 3 consecutive integers will be multiple of 5, so both 5s have to be together
so one number is 25 or a multiple of 25
let us work on remaining factors 2*2*2*2*3*13... 13*2 will give us 26 and 2*2*2*3 will give 24
so 3 integers = 24*25*26
sum of square = \(24^2+25^2+26^2=(25-1)^2+25^2+(25+1)^2=25^2-2*25+1+25^2+25^2+2*25+1=3*25^2+2=3*625+2=1875+2=1877\)
D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If the product of three consecutive positive integers is 15600 then &nbs [#permalink] 07 Sep 2018, 04:33
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