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

Question

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

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

chetan2u · Accepted Answer

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

Anigr16 · Answer

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!!

ramyatang · Answer

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

Malar95 · Answer

Common sense here.
I has to be either 3, 5 or 7.
The number is above 200 so 3 is out. 5 is also out since now we're going into the 300 range, a palindrome that ends with 2 isnt a prime number. So only available option is 7.
I honestly didnt find the real value. Just tried to use common sense and cancelling it out.

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

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

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