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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.  [#permalink]

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New post Updated on: 20 Jul 2018, 23:11
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Question Stats:

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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

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Originally posted by EgmatQuantExpert on 20 Jul 2018, 05:21.
Last edited by EgmatQuantExpert on 20 Jul 2018, 23:11, edited 2 times in total.
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A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post Updated on: 23 Jul 2018, 05:44

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.

Answer: B
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Originally posted by EgmatQuantExpert on 20 Jul 2018, 05:23.
Last edited by EgmatQuantExpert on 23 Jul 2018, 05:44, edited 2 times in total.
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 20 Jul 2018, 06:20
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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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 20 Jul 2018, 10:44
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
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 20 Jul 2018, 23:26
Hey kunalcvrce,

Your answer is correct.
But, this question can be done very quickly.

Do you want to give another try?

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

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New post 20 Jul 2018, 23:28
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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New post 20 Jul 2018, 23:30
EgmatQuantExpert wrote:
Hey kunalcvrce,

Your answer is correct.
But, this question can be done very quickly.

Do you want to give another try?

Regards,
Ashutosh
e-GMAT


EgmatQuantExpert Aditya has answered in better way ..above


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

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New post 21 Jul 2018, 01:50
Why it should not be 9*9*8 or 9*10*10 (Repetetion of digits allowed)?
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 21 Jul 2018, 02:31
EgmatQuantExpert wrote:
Hey kunalcvrce,

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

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New post 21 Jul 2018, 09:21
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
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 21 Jul 2018, 09:34
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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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 21 Jul 2018, 09:36
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


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

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New post 21 Jul 2018, 09:57
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.
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 23 Jul 2018, 05:56
Hello everyone,

Thanks for participation.

We have posted the official answer to the question.

Regards,
Ashutosh
e-GMAT
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Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



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Re: A palindrome is a number that reads the same forward and backward. &nbs [#permalink] 23 Jul 2018, 05:56
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