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29 Mar 2019, 01:57
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (02:08) correct
20%
(02:25)
wrong
based on 79
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
29 Mar 2019, 02:32
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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.
Answer: E
29 Mar 2019, 02:39
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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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