7 added 33 characters in body
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R, 88 83 77 7171 70 bytes

I'm sure that this can be improved ... and it was with credit to @flodel. A further couple of bytes saved thanks to a suggestion from @njnnja and another from @J.Doe

x=y=1:100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';write(y[x],''1)

R, 88 83 77 71 bytes

I'm sure that this can be improved ... and it was with credit to @flodel. A further couple of bytes saved thanks to a suggestion from @njnnja

x=y=1:100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';write(y[x],'')

R, 88 83 77 71 70 bytes

I'm sure that this can be improved ... and it was with credit to @flodel. A further couple of bytes saved thanks to a suggestion from @njnnja and another from @J.Doe

x=y=1:100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';write(y[x],1)
6 Shorter answer to same question in "R language"
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R, 88 83 7777 71 bytes

I'm sure that this can be improved ... and it was with credit to @flodel.

x=1:100;i=!x%%3;j=!x%%5;x[i]="Fizz";x[j]="Buzz";x[i&j]="FizzBuzz";write(x,"")

I don't have enough reputation to add a comment so I hope I'll be forgiven for editing here instead A further couple of adding a new answer. How about 74 bytes: saved thanks to a suggestion from @njnnja

x=y=1:100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';cat100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';write(y[x],sep='\n''')

R, 88 83 77 bytes

I'm sure that this can be improved ... and it was with credit to @flodel.

x=1:100;i=!x%%3;j=!x%%5;x[i]="Fizz";x[j]="Buzz";x[i&j]="FizzBuzz";write(x,"")

I don't have enough reputation to add a comment so I hope I'll be forgiven for editing here instead of adding a new answer. How about 74 bytes:

x=y=1:100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';cat(y[x],sep='\n')

R, 88 83 77 71 bytes

I'm sure that this can be improved ... and it was with credit to @flodel. A further couple of bytes saved thanks to a suggestion from @njnnja

x=y=1:100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';write(y[x],'')
5 Shorter answer to same question in "R language"
source | link

R, 88 83 77 bytes

I'm sure that this can be improved ... and it was with credit to @flodel.

x=1:100;i=!x%%3;j=!x%%5;x[i]="Fizz";x[j]="Buzz";x[i&j]="FizzBuzz";write(x,"")

I don't have enough reputation to add a comment so I hope I'll be forgiven for editing here instead of adding a new answer. How about 74 bytes:

x=y=1:100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';cat(y[x],sep='\n')

R, 88 83 77 bytes

I'm sure that this can be improved ... and it was with credit to @flodel.

x=1:100;i=!x%%3;j=!x%%5;x[i]="Fizz";x[j]="Buzz";x[i&j]="FizzBuzz";write(x,"")

R, 88 83 77 bytes

I'm sure that this can be improved ... and it was with credit to @flodel.

x=1:100;i=!x%%3;j=!x%%5;x[i]="Fizz";x[j]="Buzz";x[i&j]="FizzBuzz";write(x,"")

I don't have enough reputation to add a comment so I hope I'll be forgiven for editing here instead of adding a new answer. How about 74 bytes:

x=y=1:100;y[3*x]='Fizz';y[5*x]='Buzz';y[15*x]='FizzBuzz';cat(y[x],sep='\n')
4 deleted 91 characters in body
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3 added 95 characters in body
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2 added 50 characters in body
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