A palindrome is a number that reads the same forward or backward, such

Question

A palindrome is a number that reads the same forward or backward, such as 757. Two three digit palindromes have a difference of 11, with their units digits summing to 11. The sum of the digits of both palindromes is

A. 15
B. 19
C. 23
D. 27
E. 31

A. 15
B. 19
C. 23
D. 27
E. 31

omkartadsare · Accepted Answer

Sum of units digits is 11. Hence the sum of two numbers will have 1 at the unit's place. Only option E satisfies this. Hence 'E'.

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altairahmad · Answer

Can someone post the quickest solution to this ? It took me 5 minutes to arrive at the correct answer.

vivek2611 · Answer

Sum of units digits should be 11 and difference of both numbers should be 11.

Units digits of both numbers can be (9,2) (8,3) (7,4) (6,5).. 
Remember, the difference should be 11. So, we are looking for a units digits set from the above whose difference is 1.

That is (6,5)

Since the numbers are palindromes we have
6X6
5Y5

And as the difference of both numbers is 11.. 606 and 595 should be the numbers, Sum of all digits is 31

IMO E.

EgmatQuantExpert · Answer

Solution 
 
  Given  
 • Two three digit palindromes have a difference of 11, with their units digits summing to 11.

To find  
 • The sum of the digits of both palindromes.

Approach and Working out   
Let the three-digit palindromes be aba and pqp, where a and b are the digits of the 3-digit number abc, while p and q are the digits of the 3-digit number pqp.
Let’s assume that aba > pqp. 
 • Since aba - pqp = 11, we have either a = p or a = p + 1, else difference between two 3-digit numbers will be at least 100.

We also have 100a + 10b + a – (100p + 10q + p) = 11, since the difference between the palindromes is 11.
Therefore, 101(a – p) + 10(b – q) = 11.

Since the sum of the units digit = 11, we have a + p = 11.
 • If a = p, both a and p cannot represent the digits.
• Thus, a = p + 1.
• Thus, p + p + 1 = 11.
• We get, a = 6, p = 5. 
Using the first relation, we get, 101(1) + 10 (b-q) 11.
 • Thus, 90 = 10(q -b)
• q – b = 9 
The difference between the tens digit = 9.
 • The maximum difference between the two single digits = 9 – 0 = 9.
• Thus, q – b = 9 represents the maximum difference.
• Thus q must be 9 while b must be 0.

Therefore, the numbers are aba = 606, and pqp = 595.
The sum of the digits of the palindrome = 6 + 6 + 0 +5 + 5 + 9 = 31.

Correct Answer: Option E

rvgmat12 · Answer

A palindrome is a number that reads the same forward or backward, such as 757. Two three digit palindromes have a difference of 11, with their units digits summing to 11. The sum of the digits of both palindromes is

A. 15
B. 19
C. 23
D. 27
E. 31

Clue = Sum of units digit = 11 and difference is 11

So they must be 6x6 and 5y5

6x6-5y5 = 11 so they must be 606 and 595

Sum of digits = 12+10+9 = 31

E

aparnananya · Answer

why cant we take other numbers like 636 and 525

Bunuel · Answer

Because the difference between those number is not 11.

A palindrome is a number that reads the same forward or backward, such

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