Beat The GMAT Math Challenge Question

[sanju09]

A palindrome is a word that is read the same backwards and forwards. For example, the words "GRERG", "PPOPP", and "KKKKK" are all palindromes. How many 5-letter palindromes can be created using the letters Q, R, S, T, U, V, W, X, Y, Z?
(A) 500
(B) 1000
(C) 1200
(D) 1500
(E) 1800

Inspired by Beat The GMAT Math Challenge Question - October 4, 2010

[cans]

words - Q-Z total 10
if we select letter for 1st position, 5th is filled by that only
similarly letter for 2nd position is same as letter for 4th position
And letter for 3rd position.
So -----
for 1st we have 10 options
for 2nd we have 10 options
for 3rd we have 10 options
for 4th only 1 option (same as 2nd)
for 5th only 1 option (same as 1st)
Total = 10*10*10*1*1 = 1000
IMO B

[sanju09]

words - Q-Z total 10
if we select letter for 1st position, 5th is filled by that only
similarly letter for 2nd position is same as letter for 4th position
And letter for 3rd position.
So -----
for 1st we have 10 options
for 2nd we have 10 options
for 3rd we have 10 options
for 4th only 1 option (same as 2nd)
for 5th only 1 option (same as 1st)
Total = 10*10*10*1*1 = 1000
IMO B

kewl

[vikram4689]

5 places to be filled , 2 are fixed because of palindrome property

filling 3 places using 10 different options = 10*10*10 = 1000