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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # A number is a palindrome if it reads exactly the same from r  Question banks Downloads My Bookmarks Reviews Important topics
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A number is a palindrome if it reads exactly the same from r [#permalink]
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Expert's post 00:00

Question Stats: 53% (00:58) correct 46% (01:12) wrong based on 185 sessions

A number is a palindrome if it reads exactly the same from right to left as it does from left to right. For example. 959 and 24742 are palindromes.

 Quantity A Quantity B The probability that a 3-digit number chosen at random is a palindrome $$\frac{1}{10}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Last edited by chetan2u on 18 Dec 2018, 07:39, edited 1 time in total.
Corrected the Q Intern Joined: 21 May 2017
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
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We have a total of 900 three dig #'s between 100 and 999.
Starting with 101, 111, 121, 131, 141, 151, 161, 171, 181, 191 we've got 10 numbers on each hundreds (100's, 200's...and so go on until 900's)

Therefore, we have a total of 10*9= 90 palindromes between 100 and 999. The probability is 90/900 = 1/10 Intern Joined: 26 Dec 2017
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
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We can use permutation

total numbers 9 x 10 x 10=900

now observer 101 121 202 232 whatever the 1st digit the third digit has to be same and middle term can be any.So total possible ways are:

9 x 10 x 1 (1 because it is fixed due to the 1st digit.)

so 9*10*1/(9*10*10) =1/10
Intern Joined: 19 Mar 2018
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
A number is a palindrome if it reads exactly the same from right to left as it does from left to right. For example. 959 and 24742 are palindromes.

Quantity A

The probability chat a 3-digit number chosen at random is a palindrome
Qty B = 1/10
To me the answer was D

In Qty A there is no mention of what the denominator is: that is how many 3 digit palindromes out of 100 - 999 (only 3 digits) or 100 - 9999 (4 digit numbers). So the probability would differ.

Can someone explain why D is wrong?
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
Nice one. The important part is to figure out how many palindromes are there in those 900 three digit numbers.
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
Quantity A, without doubt Intern Joined: 24 Sep 2018
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
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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. Intern Joined: 24 Sep 2018
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
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A number is a palindrome if it reads exactly the same from right to left as it does from left to right. For example. 959 and 24742 are palindromes.

Quantity A

The probability chat a 3-digit number chosen at random is a palindrome
Qty B = 1/10
To me the answer was D

In Qty A there is no mention of what the denominator is: that is how many 3 digit palindromes out of 100 - 999 (only 3 digits) or 100 - 9999 (4 digit numbers). So the probability would differ.

Can someone explain why D is wrong?

4 digit numbers have nothing to do with this problem. Not sure where you got that from but the question is asking for what the probability is that a 3 digit number would be a palindome. 3 digit numbers start at 100 and end at 999. 099 is a 2 digit numbers and 1000 would be a 4 digit number, so neither is relevant to the question. The probability that a 3 digit number is a palindrome is: how many ways can a 3 digit number be a palindrome /how many 3 digit numbers are there. There is no inconsistency or obfuscatory elements to this problem and therefore D is not going to be a possible answer.
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
i Think quantity A is the answer
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
A: The probability chat a 3-digit number chosen at random is a palindrome
A 3-digit number can be between 100 and 999, we will have (999-100+1) = 900 3-digit numbers.
For a 3-digit number to be palindrome no matter what the middle number is, the first and third number should be the same, for instance 101, 111, 121, 131,…,181,191 are all 3-digit palindromes. Here the first and third number were 1, it can be 2,3,4,…,9 so we will have 9*10=90 3-digit palindrome out of all 900 3-digit numbers. Which is 90/900 = 1/10

All 3-digit palindroms:

101, 111, 121, 131,…,181,191
202,212,222,232, ….,292
.
.
909,919, ….., 999

B: 1/10

So A and B are equal.
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
9/10, 10/10, 10/10=9/10 Supreme Moderator
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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
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Expert's post
Carcass wrote:

A number is a palindrome if it reads exactly the same from right to left as it does from left to right. For example. 959 and 24742 are palindromes.

 Quantity A Quantity B The probability chat a 3-digit number chosen at random is a palindrome $$\frac{1}{10}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Let us find how many 3-digit numbers are palindrome..
so number is _ _ _ => XYX
so X can be any of the 9 digits from 1 to 9- so 9 ways
Y can be any of the 10 digits - so 10 ways
Total = 9*10=90 ways...

Total 3 digit words = 100 to 999 = (999-100)+1=900

Therefore, probability of choosing a 3-digit palindrome = $$\frac{90}{900}=\frac{1}{10}=A=B$$.

so both equal

C
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: A number is a palindrome if it reads exactly the same from r   [#permalink] 18 Dec 2018, 07:39
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