Re: A number is a palindrome if it reads exactly the same from r
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15 Oct 2018, 14:30
x-Y-x is a palindrom. Since 0-#-# would actually be a 2 digit number, we start with 1-#-#. For a 3 digit number, a palindom would be 1-(0-9)-1, 2-(0-9)-2, 3-(0-9)-3, and so on through 9-(0-9)-9. (0-9) is 0, 1,2,3,4,5,6,7,8,9 ...this is 10 possible answers. Therefore, there are 10 possible answers for 1-#-1, 10 possible for 2-#-2, 10 for 3-#-3 and so on. So now you know that there are 9 possible palindrom start/end digits that have 10 possible answers each. You can think of this as 10+10+10+10+10+10+10+10+10 or 10*9, which equals 90. This is the chance of a random 3 digit numbe being a palindrom.
Next we need to figure out how many possible numbers between 100-999 there are. The answer is 900. You can think of this as "there are 100 numbers between 0-99 and 1000 numbers between 0-999, then subtracting 100 from 1000 since we starts at 100 (skipping 0-99)."
Using the chance of the event (a 3 digit palindrome) / the number of possible 3 digit numbers we get the probability. So, 90/900. 90/900 can be simplified to 1/10. Therefore, A is 1/10.
Now for the final GRE answer, asking if A>B, A<B, A=B, or Cannot be determined (D), we compare the value of A (1/10) to B (1/10) and can see clearly that the answer is C, the two values are equal.
ANSWER: C, the two quantities are equal.