How many numbers are possible between 1 to 1000 which are divisible by 4 and 6 but are not divisible

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14 Apr 2011 How many number are possible

How many numbers are possible between 1 to 1000 which are divisible by 4 and 6 but are not divisible by 12?

OPtion

1) 132
2) 259
3) 249
4) 198
5) 159
6) 158
7) 150
8) 198
9) 300
10) 478

Solution

there are printing mistake in question.
It would be
which are divisible by 4 OR 6 but are not divisible by 12?

Correct Option: 3 Best Solution (4)

A J V   13 years AGO

Between 1 to 1000 (i.e., from 2 to 999)
divisors of 4: [(999-4)/4]+1=248+1=249.
divisors of 6: [{999-6)/6]+1=165+1=166.
divisors of 12: [(996-12)/12]+1=82+1=83.
G.C.F. of 4 & 6 = 12.
Now, we should subtract the no. of divisors of 12 from divisors of 4 and 6 separately.
i.e., (249-83) + (166-83) = 166+ 83 = 249.

Like? Yes (10) | No (1)  

Bimal   13 years AGO

Such numbers are
4,6,8,16,18,20,..............988,990,992
Each set of 3 numbers repeating after adding 12 to each number.

so 83 sets up to 1000.
so total numbers are 3*83=249

Like? Yes (3) | No   

sandeep reddy m   13 years AGO

divisible by 4-->250
divisible by 6--->166
by both--->83
by 12--->83
so 250+166-83-83=250

Like? Yes (1) | No   

Sukham   13 years AGO

I have solved the question assuming that statement is How many numbers are possible between 1 to 1000 which are divisible by 4 or 6 but are not divisible by 12?

Like? Yes (1) | No (1)