A palindrome is a number that reads the same forward and backward.

Question

Permutation and Combination - Practice Question #2

2-  A palindrome is a number that reads the same forward and backward. For example, 1221 and 232 are palindromes. By using the numbers from 0-9, how many 5-digit palindromes can be created.

Options

a)  648
 b)  729
 c)  800
 d)  900
 e)  1000

To solve Question 1:    Question 1

To solve Question 3:    Question 3

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EgmatQuantExpert · Accepted Answer

Solution

Given:  
 • A palindrome is a number that reads the same forward and backward.

To find:  
 • By using the numbers from 1-9, how many 5-digit palindromes can be created

Approach and Working:

Let the 5-digit number is abcba.

So, we need to find the in how many we can fill a, b, and c since the last two digits will take the same number.
 • a can take 9 numbers from 1-9.
• b can take 10 numbers from 0-9.
• c can take 10 numbers from 0-9.

Thus, way to form a 5-digit palindrome number= 9 * 10 * 10 *1 *1= 900.

Hence, the correct answer is option D.

Answer: D

kunalcvrce · Answer

I am getting 5 arrangements

ABCBA- Total arrangement A(10)*B(9)*C(8)=720 , A can be selected in 10,b in 9 and C in 8 ways
ABBBA- Total arrangement A(10)*B(9)=90
ABABA-Total arrangement A(10)*B(9)=90
AAAAA- Total arrangement A(10)=10
ABBBA-Total arrangement A(10)*B(9)=90

Total=720 +90+90+90+10=1000
Considering 0 also since its not telling 5 digit number . correct me if i am wrong

Jasveensingh · Answer

900?

- - - - - 5 places to filled. 1 blank can be filled in 9 ways.(1-9) last blank in 1 way as it has to be the same number as the 1 blanck. 2 blank can be filled in 10 ways (0-9). similarly 4 blank can be filled in 1 way only. lastly the 3 blank can also be filled in 10 ways
so 9*10*10=900

EgmatQuantExpert · Answer

Hey  kunalcvrce ,

I have one question.

Can A be 0??

Regards,
Ashutosh

thefibonacci · Answer

Number is of the form abcde 
a can be filled in 9 ways (1-9)
b can be filled in 10 ways (0-9)
c can be filled in 10 ways (0-9)
d=b, so 1 way
e=a, so 1 way
total = 9*10*10*1*1 = 900

EgmatQuantExpert · Answer

Hello everyone,

Thanks for participation.

We have posted the official answer to the question.

Regards,
Ashutosh
e-GMAT

generis · Answer

EgmatQuantExpert  , a couple of items are inconsistent.

It appears that Question #2: 
1) ought to list 0-9 as the digits that are available in both topic threads (the  solution  prompt needs to be edited to match original); 
2) ought to have a calculation error corrected.

Issues 
(1) 0-9 or 1-9?
In the original prompt for Q #2, the available digits are integers 0-9. In the solution prompt (please see highlights above), both (1-9) and (0-9) are listed.

The original prompt for Question #2 that lists 0-9 is  HERE  
(2) the second post on Q#2 solution has a calculation error, although the OA is listed correctly.
 
(9 * 10 * 10 * 1 * 1) =  900,  not 729.

It appears that Questions #1 and #2 got mixed up. The answer to Question 1  HERE,  (answer is  HERE ) is 729. 
In Question #1, the digits are limited to 1-9.

I think Q#2
-- needs to state that integers are 0-9 in all posts and
-- needs to have the written answer changed to 900

Would you please correct the inconsistencies?

Archit3110 · Answer

EgmatQuantExpert  :

quoting your line  
Thus, way to form a 5-digit palindrome number= 9 * 10 * 10 *1 *1= 729. 
 it should be 900 not 729..

EgmatQuantExpert · Answer

Hey  Archit3110 ,
We have made the changes.
Thanks

Kritisood · Answer

@experts in this question repetition of digits is allowed. are we to assume if the question doesn't mention specifically that repetition isn't allowed then it is?

robu1 · Answer

If not specifically mentioned, we will consider ‘with replacement ‘

dimri10 · Answer

May I ask if the possibility of 11111 22222 etc. Is not considered

Posted from my mobile device

Bunuel · Answer

9*10*10*1*1 will also give all numbers with repeated digits.

10 in 9* 10 *10*1*1, means that the second digit can be any, so it can be the same as the first and another 10 in 9*10* 10 *1*1, means that the third digit can be any, so it can be the same as the first and the second.

luisdicampo · Answer

Deconstructing the Question

A 5-digit palindrome reads the same forward and backward.

So every valid number must have the form   ABCBA  .

The key idea is that once the first 3 digits are chosen, the last 2 digits are forced.

Step-by-step

The first digit   A   cannot be 0, because the number must have 5 digits.

So  A  has  9  choices.

The second digit   B   can be any digit from 0 to 9.

So  B  has  10  choices.

The third digit   C   can also be any digit from 0 to 9.

So  C  has  10  choices.

Then the fourth digit must match  B , and the fifth digit must match  A , so there are no new choices there.

Total palindromes:

9 \cdot 10 \cdot 10 = 900

Answer: 900

A palindrome is a number that reads the same forward and backward.

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A palindrome is a number that reads the same forward and backward.

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