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A palindrome is a number that reads the same front-to-back as it does

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Math Expert
Joined: 02 Sep 2009
Posts: 62395
A palindrome is a number that reads the same front-to-back as it does  [#permalink]

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29 Feb 2016, 11:37
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A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 200 that is both a prime and a palindrome. What is the sum of the digits of p?

A) 3
B) 4
C) 5
D) 6
E) 7

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Joined: 23 Jan 2015
Posts: 34
Location: India
Concentration: Operations
WE: Information Technology (Computer Software)
Re: A palindrome is a number that reads the same front-to-back as it does  [#permalink]

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29 Feb 2016, 12:01
Ans E
313 is the smallest integer after 200

It cant start with 2 as being a palindrome, it should also end with 2 making it non-prime
the smallest number after that : 303 divisible by 3
next 313 which is prime!!
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Joined: 15 Feb 2016
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Re: A palindrome is a number that reads the same front-to-back as it does  [#permalink]

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02 Mar 2016, 18:52
Bunuel wrote:
A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 200 that is both a prime and a palindrome. What is the sum of the digits of p?

A) 3
B) 4
C) 5
D) 6
E) 7

Given that p is smallest integer greater than 200 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y

We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
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Joined: 02 Aug 2009
Posts: 8296
Re: A palindrome is a number that reads the same front-to-back as it does  [#permalink]

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02 Mar 2016, 19:16
4
Bunuel wrote:
A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 200 that is both a prime and a palindrome. What is the sum of the digits of p?

A) 3
B) 4
C) 5
D) 6
E) 7

HI,

The answer lies in the choices given without actualy looking/ carrying out any intensive calculations..

Info from Q--

1) the number is greater than 200, so it is atleast a 3-digit number..

solution

1) working on 3-digits number, the number cannot be in 200s, since all Palindromes in 200s will be even number and thus Non - Prime..
2) So, if its a 3-digit number and more than 300 now, the sum of digits in palindrome will atleast be 6.
3) only D and E are left..
4) In D, as the sum is multiple of 3, it is not prime..
5) the smallest/only 3-digit number with 7 as sum is 313..
6) check this for Prime..
ans E

Note-

Its very important we check for PRIMEability..
had 313 been not prime, we would have started checking 4-digits number

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Re: A palindrome is a number that reads the same front-to-back as it does  [#permalink]

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15 Jul 2017, 02:30
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Re: A palindrome is a number that reads the same front-to-back as it does   [#permalink] 15 Jul 2017, 02:30
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