A palindrome, like 12321, remains the same when its digits are reverse

Question

A palindrome, like 12321, remains the same when its digits are reversed. If x and x+32 are three-digit and four-digit palindromes, respectively, what is the sum of the digits of x?

A. 18
B. 24
C. 28
D. 32
E. 36

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A palindrome, such as  12321 , is a number that remains the same when its digits are reversed. The numbers  x  and  x+32  are three-digit and four-digit palindromes, respectively. What is the sum of the digits of  x ?

ramiav · Answer

xyx
+32
= nmmn

nm needs some overflow so X + 1 is 10
so X should be 9

9y9 + 32 = 1001 so y should be 6
and 9+9+6 = 24

VivekSri · Answer

Aryaa03 · Answer

Sol:  IMO- Option-B 
If x is a 3 digit number and x + 32 is a four digit number, then :

x + 32 > 1000 
or x > 968

As the hundred's place digit is 9, unit digit can only be a 9 for it to be a palindrome
So only options for x are 969, 979 , 989 and 999
1) 969 + 32 = 1001 (Which is palindrome)
2) 979 + 32 = 1011 (Not a palindrome)
3) 989 + 32 = 1021 (Not a palindrome)
4) 999 + 32 = 1031 (Not a palindrome)

Thus, x = 969
and Sum of digits = 24

sachi-in · Answer

This is what the question says.

A   B  A

+ 3 2
______________
C  D  D  C

Now we know at max the leftmost digit of CDDC can be 1. ( why ? because max value of A can be 9 )

Now since CDDC is a 4 digit number C must be 1 and not 0.

So ABA is 9B9. And CDDC is 1DD1

Now we know that 9 + 2 = 11 ( rightmost digits of ABA ).

Looking at leftmost digits of ABA / 9B9 :
A + 1 = D or D = 0 ( since A = 9 )

And now we know :
B + 4 = 10 + D
B = 6

bumpbot · Answer

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A palindrome, like 12321, remains the same when its digits are reverse

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A palindrome, like 12321, remains the same when its digits are reverse

Prep Toolkit

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