How many 5 digit palindromes can be made using the digits 0 to 6 with repetition?

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e-GMAT Representative

Joined: 04 Jan 2015

Posts: 3759

A palindrome is a number that reads the same forward and backward. [#permalink]

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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

To read our article: Must Read Articles and Practice Questions to score Q51 !!!!

_________________

Originally posted by EgmatQuantExpert on 20 Jul 2018, 04:24.
Last edited by chetan2u on 21 Jul 2018, 03:53, edited 3 times in total.

Shifted the topic from DS to PS

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Joined: 04 Jan 2015

Posts: 3759

A palindrome is a number that reads the same forward and backward. [#permalink]

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
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Re: A palindrome is a number that reads the same forward and backward. [#permalink]

EgmatQuantExpert wrote:

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 read our article: Must Read Articles and Practice Questions to score Q51 !!!!

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

Originally posted by kunalcvrce on 20 Jul 2018, 05:28.
Last edited by kunalcvrce on 20 Jul 2018, 06:30, edited 1 time in total.

Intern

Joined: 30 Apr 2017

Posts: 3

Re: A palindrome is a number that reads the same forward and backward. [#permalink]

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

e-GMAT Representative

Joined: 04 Jan 2015

Posts: 3759

Re: A palindrome is a number that reads the same forward and backward. [#permalink]

Hey kunalcvrce,

I have one question.

Can A be 0??

Regards,
Ashutosh
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Joined: 22 Jan 2014

Posts: 142

WE:Project Management (Computer Hardware)

Re: A palindrome is a number that reads the same forward and backward. [#permalink]

EgmatQuantExpert wrote:

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

To read our article: Must Read Articles and Practice Questions to score Q51 !!!!

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
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Illegitimi non carborundum.

e-GMAT Representative

Joined: 04 Jan 2015

Posts: 3759

Re: A palindrome is a number that reads the same forward and backward. [#permalink]

Hello everyone,

Thanks for participation.

We have posted the official answer to the question.

Regards,
Ashutosh
e-GMAT
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Joined: 22 May 2016

Posts: 5420

A palindrome is a number that reads the same forward and backward. [#permalink]

EgmatQuantExpert wrote:

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= 729.

Hence, the correct answer is option D.

Answer: D

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

Quote:

By using the numbers from 0-9, how many 5-digit palindromes can be created.

(2) the second post on Q#2 solution has a calculation error, although the OA is listed correctly.

Quote:

Thus, way to form a 5-digit palindrome number= 9 * 10 * 10 *1 *1= 729.

(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?
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Re: A palindrome is a number that reads the same forward and backward. [#permalink]

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 wrote:

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= 729.

Hence, the correct answer is option D.

Answer: D

e-GMAT Representative

Joined: 04 Jan 2015

Posts: 3759

Re: A palindrome is a number that reads the same forward and backward. [#permalink]

Hey Archit3110,
We have made the changes.
Thanks
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Location: India

Re: A palindrome is a number that reads the same forward and backward. [#permalink]

@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?

Manager

Joined: 08 Jul 2017

Posts: 101

Re: A palindrome is a number that reads the same forward and backward. [#permalink]

Kritisood wrote:

@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?

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

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Re: A palindrome is a number that reads the same forward and backward. [#permalink]

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

Posted from my mobile device

Math Expert

Joined: 02 Sep 2009

Posts: 87762

Re: A palindrome is a number that reads the same forward and backward. [#permalink]

dimri10 wrote:

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

Posted from my mobile device

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.
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Re: A palindrome is a number that reads the same forward and backward. [#permalink]

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Re: A palindrome is a number that reads the same forward and backward. [#permalink]

10 Jul 2022, 23:14

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