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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2568
A palindrome is a number that reads the same forward and backward.  [#permalink]

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Updated on: 20 Jul 2018, 22:11
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:24) correct 29% (01:31) wrong based on 109 sessions

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Permutation and Combination - Practice Question #1

1-A palindrome is a number that reads the same forward and backward. For example, 1221 and 232 are palindromes. By using the numbers from 1-9, how many 5-digit palindromes can be created.

Options

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

To solve Question 2: Question 2

To solve Question 3: Question 3

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

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Originally posted by EgmatQuantExpert on 20 Jul 2018, 04:21.
Last edited by EgmatQuantExpert on 20 Jul 2018, 22:11, edited 2 times in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2568
A palindrome is a number that reads the same forward and backward.  [#permalink]

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Updated on: 23 Jul 2018, 04:44

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 9 numbers from 1-9.
• c can take 9 numbers from 1-9.

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

Hence, the correct answer is option B.

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Originally posted by EgmatQuantExpert on 20 Jul 2018, 04:23.
Last edited by EgmatQuantExpert on 23 Jul 2018, 04:44, edited 2 times in total.
Manager
Joined: 05 Feb 2016
Posts: 157
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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20 Jul 2018, 05:20
1
EgmatQuantExpert wrote:
Permutation and Combination - Practice Question #1

1-A palindrome is a number that reads the same forward and backward. For example, 1221 and 232 are palindromes. By using the numbers from 1-9, 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(9)*B(8)*C(7)=504 , A can be selected in 9,b in 8 and C in 7 ways
ABBBA- Total arrangement A(9)*B(8)=72
ABABA- Total arrangement A(9)*B(8)=72
AAAAA- Total arrangement A(9)=9
ABBBA- Total arrangement A(9)*B(8)=72

Total=504+72+72+72+9=729
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Joined: 06 May 2018
Posts: 8
Location: India
WE: Information Technology (Consulting)
Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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20 Jul 2018, 09:44
Since , there are total 5 digits.We need to worry about just 3 digits .
_ _ _ _ _
9 9 9 1 1 hence , total =9*9*9=729
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2568
Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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20 Jul 2018, 22:26
Hey kunalcvrce,

But, this question can be done very quickly.

Do you want to give another try?

Regards,
Ashutosh
e-GMAT
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Manager
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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20 Jul 2018, 22:28
Yes..I sure want to try

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

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20 Jul 2018, 22:30
EgmatQuantExpert wrote:
Hey kunalcvrce,

But, this question can be done very quickly.

Do you want to give another try?

Regards,
Ashutosh
e-GMAT

Sent from my iPhone using GMAT Club Forum mobile app
Manager
Joined: 21 Jul 2012
Posts: 90
Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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21 Jul 2018, 00:50
Why it should not be 9*9*8 or 9*10*10 (Repetetion of digits allowed)?
Intern
Joined: 08 Jul 2017
Posts: 25
GMAT 1: 620 Q48 V29
Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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21 Jul 2018, 01:31
EgmatQuantExpert wrote:
Hey kunalcvrce,

But, this question can be done very quickly.

Do you want to give another try?

Regards,
Ashutosh
e-GMAT

Palindrome = xyzyx
X,Y, Z each can take 9 values
9x9x9= 729
Intern
Joined: 28 Oct 2017
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Location: India
Schools: ISB '20 (WL), IIM (A)
GMAT 1: 640 Q47 V32
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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21 Jul 2018, 08:21
The 5 digit palindrome has to be as simple as XYZYX, i.e. consist of only 3 numbers.

X can be selected in 9 ways
Y can be selected in 9 ways
Z can be selected in 9 ways

So, total palindroms would be 9X9X9 = 729
Intern
Joined: 03 Apr 2018
Posts: 7
Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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21 Jul 2018, 08:34
Shouldn't it be 900?

1st digit : 9 ways (1-9)
2nd digit: 10 ways (0-9)
3rd digit: 10 ways (0-9)
4th digit : 1 way
5th digit : 1 way

Any clarification will be appreciated!
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Location: India
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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21 Jul 2018, 08:36
greenisthecolor wrote:
Shouldn't it be 900?

1st digit : 9 ways (1-9)
2nd digit: 10 ways (0-9)
3rd digit: 10 ways (0-9)
4th digit : 1 way
5th digit : 1 way

Any clarification will be appreciated!

Hi greenisthecolor

The digits are from 1-9 so 10 ways not possible

Sent from my iPhone using GMAT Club Forum mobile app
Intern
Joined: 03 Apr 2018
Posts: 7
A palindrome is a number that reads the same forward and backward.  [#permalink]

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21 Jul 2018, 08:57
kunalcvrce wrote:
greenisthecolor wrote:
Shouldn't it be 900?

1st digit : 9 ways (1-9)
2nd digit: 10 ways (0-9)
3rd digit: 10 ways (0-9)
4th digit : 1 way
5th digit : 1 way

Any clarification will be appreciated!

The digits are from 1-9 so 10 ways not possible

Oh yeah. Silly me. I am doing similar mistakes more often than i'd like to.
Thanks!
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2568
Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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23 Jul 2018, 04:56
Hello everyone,

Thanks for participation.

We have posted the official answer to the question.

Regards,
Ashutosh
e-GMAT
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GMAT Tutor
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Posts: 621
Location: India
Concentration: Finance, Marketing
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GMAT 1: 700 Q51 V31
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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15 Aug 2018, 02:56
Top Contributor
Thank you.
EgmatQuantExpert wrote:
Permutation and Combination - Practice Question #1

1-A palindrome is a number that reads the same forward and backward. For example, 1221 and 232 are palindromes. By using the numbers from 1-9, how many 5-digit palindromes can be created.

Options

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

To solve Question 2: Question 2

To solve Question 3: Question 3

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

_________________

Ankit

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Re: A palindrome is a number that reads the same forward and backward.   [#permalink] 15 Aug 2018, 02:56
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