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A number is a palindrome if it reads exactly the same from r [#permalink]
26 Apr 2017, 02:23
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46% (01:12) wrong based on 199 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 3digit 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.
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Last edited by chetan2u on 18 Dec 2018, 07:39, edited 1 time in total.
Corrected the Q




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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
21 May 2017, 13:18
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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



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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
05 Jan 2018, 00:29
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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



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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
16 Sep 2018, 23:20
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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 3digit 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]
29 Sep 2018, 10:35
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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]
10 Oct 2018, 21:20
Quantity A, without doubt



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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
15 Oct 2018, 14:30
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xYx 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(09)1, 2(09)2, 3(09)3, and so on through 9(09)9. (09) 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 100999 there are. The answer is 900. You can think of this as "there are 100 numbers between 099 and 1000 numbers between 0999, then subtracting 100 from 1000 since we starts at 100 (skipping 099)."
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.



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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
15 Oct 2018, 14:37
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Madhavi1990 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
The probability chat a 3digit 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]
23 Oct 2018, 21:20
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]
25 Nov 2018, 14:47
Answer: C
A: The probability chat a 3digit number chosen at random is a palindrome A 3digit number can be between 100 and 999, we will have (999100+1) = 900 3digit numbers. For a 3digit 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 3digit palindromes. Here the first and third number were 1, it can be 2,3,4,…,9 so we will have 9*10=90 3digit palindrome out of all 900 3digit numbers. Which is 90/900 = 1/10 All 3digit 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]
18 Dec 2018, 07:27
9/10, 10/10, 10/10=9/10
I got this answer.



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Re: A number is a palindrome if it reads exactly the same from r [#permalink]
18 Dec 2018, 07:39
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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 3digit 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 3digit 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 = (999100)+1=900 Therefore, probability of choosing a 3digit 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/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html




Re: A number is a palindrome if it reads exactly the same from r
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18 Dec 2018, 07:39





