Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 32)
32.
How many 3-digit numbers are completely divisible 6 ?
149
150
151
166
Answer: Option
Explanation:

3-digit number divisible by 6 are: 102, 108, 114,... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then tn = 996.

a + (n - 1)d = 996

102 + (n - 1) x 6 = 996

6 x (n - 1) = 894

(n - 1) = 149

n = 150

Number of terms = 150.

Discussion:
33 comments Page 3 of 4.

Ishan said:   1 decade ago
Directly, on dividing 150 by 6 gives o as a reminder and as a quotient it gives 25 so that 150 comes in the multiple of 25 in the 6 place.

150/6 = 25.

25*6 = 150.

Swathi said:   1 decade ago
149:1+4+9 = 16 it is not divisible by 6.

150:1+5+0 = 6 it is divisible by 6.

151:1+5+1 = 7 not divisible by 6.

166:1+6+6 = 13 not divisible by 6.

Ans :150 (B).

Udaya santhi said:   1 decade ago
6 written as 2*3.

The number completely divisible by both numbers 2&3.

If the number is divisible by 2 that number should be an even.

If the number is divisible by 3 then taken sum of digits.

Option verification:

Only two even numbers are there 150 & 166.

These two numbers are divisible by 2.

1+5+0 = 6(which is divisible by 3), 1+6+6 = 13(which is not divisible by 3).

Hence 150 is the answer.

Harpreet said:   1 decade ago
@Ashish total numbers divisible by 8 comes 112 & not 113.

Ashish said:   1 decade ago
If we want to find how many numbers present in 3 digit no which is divisible by any number. Then here is method.

Eg: How many 3-digit numbers are completely divisible 8 ?

Answer:

1000/8=125.

100/8=12 with remainder 4.

125-12=113.

So 113 numbers are divisible from 100 to 999 by 8.

Lalit said:   1 decade ago
Another short technique is last 3 digit no is 999 so we divide 999/6= 166 we don't consider decimal part. Now, we only need 3 digit number so 100/6= 16 therefore, 166-16=150 answer.

166 is the total number divisible by 6. We subtracted 100 because before 100 there is only 2 digit number divide by 6.

Gis said:   1 decade ago
@sworna
999-100+1 is taken based on arithmetic progression . last 3-digit no: is 999 and first 3-digit no: is 100 . according to the equation n=(l-a)/d +1
here l=999,a=100, d=1
so n=(999-100)/1 +1=900
hope u can understand

Neha nagar said:   1 decade ago
@sworna

Dear sworna here +1 is because 100 is also included in three digit no we can not leave 100 here. So it will b better to solve like this....3 digit nos-2 digit nos. So that 999-99=900. Hope you have got it.

Sworna said:   1 decade ago
@Mahesh.

Why it is 999-100+1? I can't understand please help me.

Rajkin said:   1 decade ago
Thanks mahesh patel.


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