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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paragw · Answer

Smallest 4 digit palindrome is 1001
1001 - 32 = 969 (a palindrome)
Sum of digits of x is 24

SwiftMonk · Answer

1001-32=969
9+6+9=24

MarkGMATMentor · Answer

On questions involving digit values, make deductions based on the limits imposed by the prompt.

For x and x+32 to be three- and four-digit numbers, respectively, x+32 must be within 31 of 1000. Thus, the first two digits of x+32 are 1 and 0, and so the last two digits are 0 and 1. The four-digit number is 1001.

1001-32 = 969, and 9+6+9=24.

The answer is B.

Solving Using the Answer Choices: 
Alternatively, you could solve using the answer choices to help you.

For x and x+32 to be three- and four-digit numbers, respectively, x must be within 32 of 1000.

This tells you that the first digit of x is 9, and since it's a palindrome, the last digit is also 9.

If the middle digit were 9, the sum of the digits would be 27. This is the highest sum of digits possible. We can eliminate C, D, and E.

If choice A were correct, the middle digit would be 0. But 909+32 is under 1000. We can eliminate A. The answer must be B.

Either way you do it, it's important to recognize that because adding 32 changes the number from three to four digits, both numbers must be close to the "border value" of 1000. Deductions like these will help you solve digit values questions efficiently.

Rad29 · Answer

Hint is that x is a three digit number and x+32 is a four digit number (so border values). x is of the form 9x9, trying 999,989,979,969 (which works), 9+6+9=24

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards