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

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

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26 Aug 2011, 06:42
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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
[Reveal] Spoiler: OA

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

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26 Aug 2011, 09:47
enigma123 wrote:
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

First recognize you only need to consider the first two digits (because the second two are just the first two flipped)

There are 90 possibilities for the first two digits of a 4 digit number, 10-99 inclusive. Everything starting with a 1,3,5,7,9 will be odd, which is 5/9ths of the combinations.

5/9*90 = 50 C
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Re: A palindrome is a number that reads the same forward and backward, suc [#permalink]

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31 Aug 2011, 10:47
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enigma123 wrote:
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

@enigma123: Here is my explanation:

A palindrome is a number that reads the same forward and backward. Examples of four digit palindromes are 1221, 4334, 2222 etc
You basically get to choose the first two digits and you repeat them in opposite order. Say, you choose 45 as your first two digits. The next two digits are 54 and the number is 4554.
Also, you need only odd palindromes. This means that you need an odd digit at the end i.e. 1/3/5/7/9. This means that you need to start the number with an odd digit. Only then will it end with an odd digit.

In how many ways can you pick two digits such that the first one is an odd digit?
The first digit can be selected in 5 ways.(1/3/5/7/9)
The second digit can be selected in 10 ways.(0/1/2/3...8/9)
Total = 5*10 = 50 ways
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 09 Jun 2011 Posts: 103 Re: A palindrome is a number that reads the same forward and backward, suc [#permalink] ### Show Tags 01 Sep 2011, 20:36 The question demands that in Palindrome, the first digit must be odd that is why the last digit becomes odd. For example, 1221 is a palindrome that reads same backward and forward and it is odd. So the easy way of solving it is; Take first odd digit, there are five odd digit and five different ways of selecting it The second digit can be both odd or even no restriction, therefore there are 10 different ways of selecting it The first digit can be selected in 5 ways.(1/3/5/7/9) The second digit can be selected in 10 ways.(0/1/2/3...8/9) Total = 5*10 = 50 ways The definite Answer is 50 Manager Joined: 10 Feb 2012 Posts: 71 Location: India Concentration: Marketing, Strategy GMAT 1: 640 Q48 V31 GPA: 3.45 WE: Marketing (Pharmaceuticals and Biotech) A palindrome is a number that reads the same forward and [#permalink] ### Show Tags 30 Mar 2012, 05:00 3 This post received KUDOS 14 This post was BOOKMARKED 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 Math Expert Joined: 02 Sep 2009 Posts: 39589 Re: A palindrome is a number that reads the same forward and [#permalink] ### Show Tags 30 Mar 2012, 05:05 10 This post received KUDOS Expert's post 6 This post was BOOKMARKED pratikbais wrote: 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 We want to determine how many odd 4-digit numbers like XYYX are there. Notice here that in a palindrome X and Y can be the same, for example 1111 or 3333 are also palindromes. Since, the number must be odd then the first and the last digits (X's) can take 5 values (1, 3, 5, 7, or 9) and the two middle digits (Y's) can take 10 values (0, 1, ..., 9), so total such numbers possible is 5*10=50. Answer: C. Hope it's clear. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15918 Re: A palindrome is a number that reads the same forward and [#permalink] ### Show Tags 10 Sep 2014, 00:41 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15918 Re: A palindrome is a number that reads the same forward and backward, suc [#permalink] ### Show Tags 06 Nov 2014, 02:05 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Math Expert Joined: 02 Sep 2009 Posts: 39589 Re: A palindrome is a number that reads the same forward and backward, suc [#permalink] ### Show Tags 06 Nov 2014, 05:59 enigma123 wrote: 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 Similar questions to practice: a-palindrome-is-a-number-that-reads-the-same-forward-and-129898.html a-palindrome-is-a-number-that-reads-the-same-forward-and-backward-181030.html a-palindrome-number-reads-the-same-backward-and-forward-159265.html a-palindrome-is-a-number-that-reads-the-same-forward-and-bac-161167.html Hope it helps. _________________ Senior Manager Joined: 27 Dec 2013 Posts: 305 Re: A palindrome is a number that reads the same forward and [#permalink] ### Show Tags 03 May 2015, 11:20 HI Buneul, A quick question with this problem. We can also make a palindrom out of event number also right.. such as 8228. Why does it have to be odd numbers. Sorry a very old question. pratikbais wrote: 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 _________________ Kudos to you, for helping me with some KUDOS. Math Expert Joined: 02 Sep 2009 Posts: 39589 Re: A palindrome is a number that reads the same forward and [#permalink] ### Show Tags 03 May 2015, 11:45 shriramvelamuri wrote: HI Buneul, A quick question with this problem. We can also make a palindrom out of event number also right.. such as 8228. Why does it have to be odd numbers. Sorry a very old question. pratikbais wrote: 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 Because the question specifically asks about the number of odd palindromes. _________________ Manager Joined: 18 Aug 2014 Posts: 131 Location: Hong Kong Schools: Mannheim Re: A palindrome is a number that reads the same forward and [#permalink] ### Show Tags 26 Oct 2015, 04:53 Bunuel wrote: pratikbais wrote: 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 We want to determine how many odd 4-digit numbers like XYYX are there. Notice here that in a palindrome X and Y can be the same, for example 1111 or 3333 are also palindromes. Since, the number must be odd then the first and the last digits (X's) can take 5 values (1, 3, 5, 7, or 9) and the two middle digits (Y's) can take 10 values (0, 1, ..., 9), so total such numbers possible is 5*10=50. Answer: C. Hope it's clear. Hi Bunuel, what about negative numbers? Shouldn't we multiply the result by 2 ? CEO Joined: 17 Jul 2014 Posts: 2524 Location: United States (IL) Concentration: Finance, Economics Schools: Stanford '20 GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: A palindrome is a number that reads the same forward and backward, suc [#permalink] ### Show Tags 28 Oct 2015, 18:19 2 This post received KUDOS 4 digits then the number must be in the format ABBA. A must be odd, so we have 5 possibilities for A. B can be whatever number, so it has 10 possibilities. now, combine everything: A = 5 B = 10 second B cannot be any of the 10 digits, it must be exactly as the first B, so it must be 1 combination A = must be the same as first A, so there is only 1 combination 5*10*1*1 = 50 Intern Joined: 08 Oct 2015 Posts: 11 Re: A palindrome is a number that reads the same forward and [#permalink] ### Show Tags 17 Nov 2015, 19:17 Bunuel Why is it not 2500? 5*10*10*5? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9252 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: A palindrome is a number that reads the same forward and [#permalink] ### Show Tags 17 Nov 2015, 22:17 4 This post received KUDOS Expert's post Hi dubyap, Since the 4th digit has to match the 1st digit and the 3rd digit has to match the 2nd digit, you don't have as many options as you might think. Since the palindrome has to be ODD, both the 1st and 4th digits have to be ODD and the SAME... The 1st digit could be 1, 3, 5, 7 or 9 The 4th digit must MATCH the first digit, so once you choose the 1st digit, there is ONLY ONE possible number for the 4th digit. The 2nd digit could be any of the 10 options (0 - 9, inclusive). The 3rd digit must MATCH the 2nd digit, so once you choose the 2nd digit, there is ONLY ONE possible number for the 3rd digit. Thus, there are... (5)(10)(1)(1) = 50 options GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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21 Mar 2016, 12:50
Q A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?

1. 40
2. 45
3. 50
4. 90
5. 2500

I HAVE THE ANSWER JUST NOT SATISFIED WITH THE EXPLANATION.

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

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21 Mar 2016, 13:00
umg4147 wrote:
Q A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?

1. 40
2. 45
3. 50
4. 90
5. 2500

I HAVE THE ANSWER JUST NOT SATISFIED WITH THE EXPLANATION.

Follow posting guidelines (link in my signatures), search for a question before starting a new thread, topic name should be the first few words of the question itself and add tags related to the question.

Topics merged.

Refer above for the solution.

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

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29 Mar 2017, 05:09
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Re: A palindrome is a number that reads the same forward and [#permalink]

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01 Apr 2017, 15:45
The number is in the format ABBA, but note that B can equal A.

Choices for A = 1, 3, 5, 7, 9 = 5 choices
Choices for B = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 = 10 choices

5x10=50. Note that the third and fourth numbers are dictated by the second and first numbers respectively.
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Re: A palindrome is a number that reads the same forward and [#permalink]

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22 Apr 2017, 18:55
enigma123 wrote:
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

The most convenient way to do this problem that I found was to consider the number of 4 digit numbers that begin and end with an odd number- not literally all of them but all four numbers must begin and end with 1,3,5,7,9 so if there were a matrix there would be five columns- how rows are there though, or rather possibilities under each column

There are five odd numbers that our four digit number can begin and end with hence 5 columns [1, 3, 5,7, 9]

Now,

1--1 the two numbers must match so actually from [0-9] there are ten possibilities

If there are 10 possibilities for each odd and there 5 odd numbers then there are 50 possibilities

Thus C
Re: A palindrome is a number that reads the same forward and   [#permalink] 22 Apr 2017, 18:55
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