Latest Infosys Aptitude Question SOLUTION: How many 6 digit palindromes are divisible by 8?

• Placement Papers
• /
• Infosys
• /
• Numerical Ability
• /
• Arithmetic

Infosys Question Papers: Infosys Interview Experience(10) INFOSYS Company Profile

(#M40026411) INFOSYS Numerical Ability question maths Keep an EYE

How many 6 digit palindromes are divisible by 8?

Asked In Infosys Swatcat (10 years ago)

Unsolved Read Solution (5)

Is this Puzzle helpful?   (13)   (5) Submit Your Solution Arithmetic

Read Solution (5) :

chaitanya  (10 years ago)

answer is 100


Let the 6 digit palindromic number is abccba
a≠0 , Because then the number will become a five digit number

Now let's come to the point of divisibility by 8.

When the last three digit of a number is evenly divisible by 8 then the whole number is divisible by 8.

So here if 8 divides cba then it will also divide abccba.

cba can be any number from 001 to 999 if a≠0.

So cba can't be a number which ends with 0 .

Now for knowing how many numbers from 1 to 999 is divisible by 8 we will divide 999 by 8 and take the quotient.We get 124 as quotient by dividing 999 by 8.

But as the 6 digit palindromic numbers can't end with a zero we can't take the numbers which ends with a zero.

The numbers which end with a zero can be divided by 5. Again a number which can be divided by both 5 and 8 can also be divided by 40.

From 1 to 999 there are 24 numbers which can be divided by 40.(by dividing 999 by 40 and taking the quotient.)

So there are 124−24

100 six digit palindromic numbers which can be divided by 8.

Is this solution Helpfull? Yes (41) | No (3)  

lakshmi vyshnavi  (10 years ago)

The no.of palindromes are:100
Because the 6 digit palindromes are divisible by 8.
It means that the last 3 digits are divisible by 8.
B/w 0 and 999 the no.of digits which are divisible by 8 are 124.
and the last digit should not end with 0 since it will become a 5 digit no in palindrome.
The digits which are divisible by 8 and end with 0 are 24.
Hence the total palindromes which are obtained are 124-24=100.

Is this solution Helpfull? Yes (5) | No   

Soumyabrata Sarkar  (10 years ago)

Divisibility rule of 8- last 3 digit no must be divisible by 8.
First 6 digit no which is divisible by 8 is 800(008) as 008 is divisible by 8.

Then

800(008) [8x1=8]
610(016) [8x2=16]
240(024) [8x3=24]
....
299(992) [8x124=992]

total no will be 124

6 digit palindrome no should not end with a 0.
so we have

8x5=40 [6 digit no should not be like 040040]
8x10=80 [6 digit no should not be like 080080]
8x15=120 [6 digit no should not be like 012120]
....

let n be the no of possible such no ends with a 0

Then 5+(n-1)5=120
n=24

Ans: 124-24=100

Is this solution Helpfull? Yes (1) | No   

parul jain  (10 years ago)

diMag ki band bja di.

Is this solution Helpfull? Yes (1) | No (1)  

parul jain  (10 years ago)

diMag ki band bja di.

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.