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# A palindromic number is a number that remains the same when its digits

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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A palindromic number is a number that remains the same when its digits  [#permalink]

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10 Jan 2018, 01:10
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Difficulty:

65% (hard)

Question Stats:

60% (01:10) correct 40% (01:24) wrong based on 40 sessions

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[GMAT math practice question]

A palindromic number is a number that remains the same when its digits are reversed. For example, $$16461$$ is a palindromic number. If a $$4$$ digit integer is selected randomly from the set of all $$4$$ digit integers, what is the probability that it is palindromic?

A. $$\frac{1}{20}$$
B. $$\frac{1}{50}$$
C. $$\frac{1}{60}$$
D. $$\frac{1}{90}$$
E. $$\frac{1}{100}$$

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 16 Apr 2017 Posts: 12 Re: A palindromic number is a number that remains the same when its digits [#permalink] ### Show Tags 10 Jan 2018, 02:15 1 Total 4-digit integers= 9999-1000+1= 9000. There is only one palindromic number in evey 100 nos. Therefore, total no.of palindromic= 90. Probability= 90/9000=1/100. Sent from my ONEPLUS A5010 using GMAT Club Forum mobile app Intern Joined: 06 Jan 2018 Posts: 4 Re: A palindromic number is a number that remains the same when its digits [#permalink] ### Show Tags 10 Jan 2018, 02:28 You can choose first and second digit randomly (first digit not zero). Chance that third digit equals second: 1/10. Equally, chance that fourth digit = first digit: 1/10. That 0 is not possible for first digit doesn't matter: once chosen, chance that fourth is the same = 1/10. Check: other way round: choose 3rd and 4th at random. Chance that 1st equals 4th: 0 if 4th=0 and 1/9 if 4th not 0. So: chance that first equals 4th: 1/10 *0 + 9/10 * 1/9 = 1/10. So answer: 1/10 * 1/10 = 1/100 Sent from my U FEEL PRIME using GMAT Club Forum mobile app Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6227 GMAT 1: 760 Q51 V42 GPA: 3.82 A palindromic number is a number that remains the same when its digits [#permalink] ### Show Tags 12 Jan 2018, 00:52 => 4-digit palindromic numbers have the form $$‘xyyx’$$, where $$x$$ is one of values $$1,2,…,9$$ and $$y$$ is one of values $$0,1,2,…,9.$$ So, there are $$9 * 10 = 90$$ four-digit palindromic numbers. The total number of 4-digit numbers between $$1000$$ and $$9999$$, inclusive, is $$9000 ( = 9999 – 1000 + 1 )$$. Therefore, the probability that the selected 4-digit is palindromic is $$\frac{90}{9000} = \frac{1}{100}.$$ Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: A palindromic number is a number that remains the same when its digits  [#permalink]

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16 Jan 2018, 17:48
MathRevolution wrote:
[GMAT math practice question]

A palindromic number is a number that remains the same when its digits are reversed. For example, $$16461$$ is a palindromic number. If a $$4$$ digit integer is selected randomly from the set of all $$4$$ digit integers, what is the probability that it is palindromic?

A. $$\frac{1}{20}$$
B. $$\frac{1}{50}$$
C. $$\frac{1}{60}$$
D. $$\frac{1}{90}$$
E. $$\frac{1}{100}$$

Let’s determine the number of the 4-digit palindromes. Notice that a 4-digit number is a palindrome if it’s one of the following two formats: XXXX and XYYX where X and Y represent a digit and X ≠ Y and X is nonzero.

Format 1: XXXX

We see that X can be any digit from 1 to 9, inclusive; thus, there are 9 such numbers.

Format 2: XYYX

We see that X can be any digit from 1 to 9, inclusive, and Y can be any digit from 0 to 9, inclusive (excluding digit X), so that there are 9 choices for X and 9 choices for Y; thus, the number of 4-digit number in this format is 9 x 9 = 81.

Thus, there are a total of 9 + 91 = 90 numbers in both formats. Since there are 9000 four-digit numbers (1000 to 9999 inclusive), the probability of picking a 4-digit palindrome randomly is 90/9000 = 1/100.

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Re: A palindromic number is a number that remains the same when its digits &nbs [#permalink] 16 Jan 2018, 17:48
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