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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
A palindrome, such as 83438, is a number that remains the same when it  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 83% (02:16) correct 17% (02:39) wrong based on 42 sessions

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A palindrome, such as 83438, 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?

(A) 20
(B) 21
(C) 22
(D) 23
(E) 24

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Re: A palindrome, such as 83438, is a number that remains the same when it  [#permalink]

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2

Solution

Given:
• A palindrome, such as 83438, 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.

To find:
• The sum of the digits of x.

Approach and Working:
It is given that x is 3-digit number and x + 32 is a 4-digit number.
• Therefore, max (x) = 999 and hence, max (x + 32) = 1031
• Similarly, min (x + 32) = 1000 and hence, min (x) = 968

Now, x + 32 lies between 1000 and 1031 and it is a palindrome.

In that given range, we have only one palindrome, which is 1001.
• Therefore, x + 32 = 1001
Or, x = 1001 – 32 = 969

So, sum of the digits of x = 9 + 6 + 9 = 24

Hence, the correct answer is option E.

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Re: A palindrome, such as 83438, is a number that remains the same when it  [#permalink]

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Take the lowest number of palindrome 1001 as an example of x + 32. Why the lowest? Because any higher palindrome minus 32 and the result is not equal a three digits number. 1001 - 32 = 969. Sum of x's digits is 24. E is the answer

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Re: A palindrome, such as 83438, is a number that remains the same when it  [#permalink]

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Bunuel wrote:
A palindrome, such as 83438, 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?

(A) 20
(B) 21
(C) 22
(D) 23
(E) 24

As we know adding x is a 3-digit number and x + 32 is a 4-digit number, we should start with highest 3 -digit palindrome number.

Say x = 999

so sum of digits of x = 9+9+9 = 27 (not in option)

x = 989 , therefore x + 32 = 1021 (not palindrome)

x = 979, therefore x + 32 = 1011 (not palindrome)

x = 969, therefore x + 32 = 1001 (PALINDROME)

Hence, x = 969 is the correct value of x.

Sum of digit of x = 9+6+9 = 24 (E)

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Re: A palindrome, such as 83438, is a number that remains the same when it  [#permalink]

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Bunuel wrote:
A palindrome, such as 83438, 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?

(A) 20
(B) 21
(C) 22
(D) 23
(E) 24

3 digti palindrome max = 999
999+32 ; 1031
and min 4 digit = 1000 range = 1031 to 1000
best value 1001
x = 1001-32 ; 969
sum ; 24
IMO E Re: A palindrome, such as 83438, is a number that remains the same when it   [#permalink] 29 Mar 2019, 08:06
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