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.

Answer: E

_________________

Scott Woodbury-Stewart

Founder and CEO

GMAT Quant Self-Study Course

500+ lessons 3000+ practice problems 800+ HD solutions