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# A palindrome number reads the same backward and forward

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A palindrome number reads the same backward and forward [#permalink]  06 Sep 2013, 04:54
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A palindrome is a number which reads the same when read forward as it it does when read backward. So, how many 5 digit palindromes are there?

(A) 720
(B) 800
(C) 890
(D) 900
(E) 950
[Reveal] Spoiler: OA

Last edited by arakban99 on 06 Sep 2013, 05:10, edited 1 time in total.
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Re: A palindrome number reads the same backward and forward [#permalink]  06 Sep 2013, 05:04
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arakban99 wrote:
A palindrome is a number which reads the same when read forward as it it does when read backward. So, how many 5 digit palindromes are there?

(A)720
(B)800
(C)890
(D)900
(E)950

A 5 digit palindrome would look like this : $$abcba.$$
Thus, the first digit can be filled in 9 ways(1-9), the second digit can be filled in 10 ways (0-9) and the 3rd digit can again be filled in 10 ways. The last 2 digits would just mirror the already selected digit. Thus, the no of ways : 9*10*10*1*1 = 900.
D.
_________________
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Re: A palindrome number reads the same backward and forward [#permalink]  06 Sep 2013, 05:04
Here is the official solution:

there five digit places

__ __ __ __ __

The last two depend on the first two (because the last to is the flipped version of the first two digits i.e 54145 - 45 is the flipped version of 54 so the number of ways to select the last two is 1*1

So this the total of ways to select (combination) the digits: 9 (digits 1-9, remember 0 at the start will make the number a four digit number) * 10 (0-9) * 10 (0-9) * 1 *1

= 900.

Hope it helped
_____________
Comments and KUDOS are deeply appreciated

Last edited by arakban99 on 06 Sep 2013, 05:07, edited 1 time in total.
Intern
Joined: 03 Aug 2013
Posts: 15
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Kudos [?]: 13 [0], given: 46

Re: A palindrome number reads the same backward and forward [#permalink]  06 Sep 2013, 05:06
mau5 wrote:
arakban99 wrote:
A palindrome is a number which reads the same when read forward as it it does when read backward. So, how many 5 digit palindromes are there?

(A)720
(B)800
(C)890
(D)900
(E)950

A 5 digit palindrome would look like this : $$abcba.$$
Thus, the first digit can be filled in 9 ways(1-9), the second digit can be filled in 10 ways (0-9) and the 3rd digit can again be filled in 10 ways. The last 2 digits would just mirror the already selected digit. Thus, the no of ways : 9*10*10*1*1 = 900.
D.

Yep, that's my solution too.
Math Expert
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Posts: 28781
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Kudos [?]: 47474 [1] , given: 7123

Re: A palindrome number reads the same backward and forward [#permalink]  06 Sep 2013, 06:33
1
KUDOS
Expert's post
arakban99 wrote:
A palindrome is a number which reads the same when read forward as it it does when read backward. So, how many 5 digit palindromes are there?

(A)720
(B)800
(C)890
(D)900
(E)950

_____________
Comments and KUDOS are deeply appreciated

Similar question to practice:
Quote:
A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?

A. 40
B. 45
C. 50
D. 90
E. 2500

Hope it helps.
_________________
Senior Manager
Joined: 25 Sep 2012
Posts: 278
Location: India
Concentration: Strategy, Marketing
Schools: Ivey '17
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Followers: 0

Kudos [?]: 88 [2] , given: 237

Re: A palindrome number reads the same backward and forward [#permalink]  06 Sep 2013, 07:29
2
KUDOS
if the question was without repating any digit for example 99199 is not allowed (of course e.g. like 45154 is allowed)
Hope I'm not making a fool of myself by asking this question
Math Expert
Joined: 02 Sep 2009
Posts: 28781
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Kudos [?]: 47474 [1] , given: 7123

Re: A palindrome number reads the same backward and forward [#permalink]  07 Sep 2013, 04:21
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b2bt wrote:
if the question was without repating any digit for example 99199 is not allowed (of course e.g. like 45154 is allowed)
Hope I'm not making a fool of myself by asking this question

Yes, if repetition were not allowed, then the answer would be 9*9*8 --> abcba:

9 options for a (from 1 to 9 inclusive);
9 options for b (from 0 to 9 inclusive minus the digit we used for a);
8 options for c (from 0 to 9 inclusive minus two digit we used for a and b).
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Re: A palindrome number reads the same backward and forward [#permalink]  13 Nov 2014, 10:35
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Re: A palindrome number reads the same backward and forward   [#permalink] 13 Nov 2014, 10:35
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