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Math Revolution GMAT Instructor V
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Difficulty:   55% (hard)

Question Stats: 61% (01:52) correct 39% (02:24) wrong based on 18 sessions

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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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
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Official Solution:

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. $$\frac{1}{100}$$

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 x 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 $$\frac{90}{9000} = \frac{1}{100}$$.

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Here is a better explanation.

Total no. of outcomes= 9999-999=9000 numbers of 4 digits

Favorable outcomes= 9C1 x 10C1 x 1C1 x 1C1=90
Hence , probability = 90/9000=1/100 Re: M61-02   [#permalink] 29 Oct 2018, 12:31
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# M61-02

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