Sum of all integers less than 100 which leave a remainder 1 when divide by 3 and leave a remainder 2 when divided by 4 is :-

Asked by prateekagar | 29th Oct, 2010, 12:00: AM

Expert Answer:

dear student,
ATQ,
if the integer is p
then
p-1 is a multiple of 3
numers like 4,7,10... fall in this category
and
p-2 is divisible by 4
numbers like 6,10,14...etc fall in this category.
the numbers common to both groups will occur at a gap of 3x4=12
clearly such numbers will have a gap of 12 between them.
so numbers which come under both categories are
10 ,22 ,34, 46 ,58, 70 ,82, 94
this is an A.P.with
first term =a=10
common diff= d= 12
last term=94
find the sum using the A.P. formula for sum of n terms. 

Answered by  | 29th Oct, 2010, 08:25: PM

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