Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

can you tell those numbers which are lying between 200 and 500 and divisible by 3 if digits are repeated?
Asked by aashu.60 | 01 Jul, 2015, 09:11: AM
answered-by-expert Expert Answer
1. First let's find all three digit numbers starting with '2' which are divisible by '3' when digits are repeated.
    2 _ _ .
Since digits have to be repeated, we have two possibilities: 2 _ 2 or 2 X X or 2 2 X, where X is any digit from '0' to '9'.
For 2 _ 2, for the number to be divisible by '3', the middle digit can be 2 or 5 or 8.
We get the numbers 2 2 2 , 2 5 8 , 2 8 2. Three numbers divisible by '3'.
For 2 X X, for the numbers to be divisible by '3', 'X' can be 2 or 5 or 8. But for X=2, we get the number 2 2 2, which has already been counted above. Hence, excluding that we get 2 5 5 and 2 8 8. Two numbers divisible by '3'.
For 2 2 X, for the numbers to be divisible by '3', 'X' can be 2 or 5 or 8. But for X=2, we get the number 2 2 2, which has already been counted above. Hence, excluding that we get 2 2 5 and 2 2 8. Two numbers divisible by '3'.
Hence, in total we get 3+2+2 =7 such numbers starting with '2' which are divisible by three when digits are repeated..... (1)
 
2. Next, let's find all three digit numbers starting with '3' which are divisible by '3' when digits are repeated.
   3 _ _ .
Since the digits have to be repeated, we have two possibilities: 3 _ 3 or 3 X X or  3 3 X, where X is any digit from '0' to '9'.
For 3 _ 3, for the number to be divisible by '3', the middle digit can be 0 or 3 or 6 or 9.
We get the numbers 3 0 3 , 3 3 3 , 3 6 3, 3 9 3. Four numbers divisible by '3'.
For 3 X X, for the numbers to be divisible by '3', 'X' can be 0 or 3 or 6 or 9. But for X=3, we get the number 3 3 3, which has already been counted above. Hence, excluding that we get 3 0 0, 3 6 6, 3 9 9. Three numbers divisible by '3'.
For 3 3 X, for the numbers to be divisible by '3', 'X' can be 0 or 3 or 6 or 9. But for X=3, we get the number 3 3 3 , which has already been counted above. Hence, excluding that we get 3 3 0 or 3 3 6 and 3 3 9. Three numbers divisible by '3'.
Hence, in total we get 4+3+3 =10 such numbers starting with '3' which are divisible by three when digits are repeated..... (2)
 
3
Next, let's find all three digit numbers starting with '4' which are divisible by '3' when digits are repeated.
   4 _ _ .
Since the digits have to be repeated, we have two possibilities: 4 _ 4 or 4 X X or 4 4 X, where X is any digit from '0' to '9'.
For 4 _ 4, for the number to be divisible by '3', the middle digit can be 1 or 4 or 7.
We get the numbers 4 1 4, 4 4 4, 4 7 4. Three numbers divisible by '3'.
For 4 X X, for the numbers to be divisible by '3', 'X' can be 1 or 4 or 7. But for X=4, we get the number 4 4 4, which has already been counted above. Hence, excluding that we get 4 1 1 and 4 7 7. Two numbers divisible by '3'.
For 4 4 X, for the numbers to be divisible by '3', 'X' can be 1 or 4 or 7. But for X=4, we get the number 4 4 4 , which has already been counted above. Hence, excluding that we get 4 4 1 and 4 4 7. Two numbers divisible by '3'.
Hence, in total we get 3+2+2 =7 such numbers starting with '4' which are divisible by three when digits are repeated..... (3)
 
From (1), (2) and (3), we get total number of such numbers lying between 200 and 500 as 7+10+7=24.
Answered by satyajit samal | 01 Jul, 2015, 02:25: PM
CBSE 11-science - Maths
Asked by lovemaan5500 | 02 Feb, 2019, 08:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by lovemaan5500 | 02 Feb, 2019, 08:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by yogeshkumar pathak | 31 Jan, 2019, 11:56: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
If space straight P presuperscript 2 straight n plus 1 end presuperscript subscript straight n minus 1 end subscript colon straight P presuperscript 2 straight n minus 1 end presuperscript subscript straight n equals 3 colon 5 comma space then space find space straight n.
Asked by Topperlearning User | 02 Jun, 2015, 01:59: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×