Numbers
To determine if a number is divisible by 7, take the last digit off the number, double it and subtract the doubled number from the remaining number. If the result is evenly divisible by 7 (e.g. 14, 7, 0, -7, etc.), then the number is divisible by seven. This may need to be repeated several times. Example: Is 3101 evenly divisible by 7?
310 - take off the last digit of the number which was 1
-2 - double the removed digit and subtract it
308 - repeat the process by taking off the 8
-16 - and doubling it to get 16 which is subtracted
14 - the result is 14 which is a multiple of 7
Which is the smallest number which when decreased by 5 is divisible by 21,27,33,55
a)1490 b)10400 c)15490 d)none
sol:21=7*3
27=9*3
33=3*11
55=5*11
it must be divisible by 3,7,9,11
a)1490-5=1485
148-10=138
13-16=-3 so not divisible by 7
b)10400-5=10395
1039-10=1029
102-18=84
8-8=0 therefore the number is divisible by 7
c)15490-5=15485
15485-10=15475
1547-10=1537
153-14=139
13-18=-5 not divisible by 7
hence b is correct answer as it is divisible by 3,7,9,11
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