Beat The GMAT Math Challenge Question

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Jun 03, 2011 1:20 am

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

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Source: Beat The GMAT — Problem Solving | Fri Jun 03, 2011 1:20 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Fri Jun 03, 2011 1:24 am

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

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Jun 03, 2011 1:50 am

cans wrote: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

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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vikram4689: Legendary Member; Posts: 1325; Joined: Sun Nov 01, 2009 6:24 amFollowed by: 14 members; Thanked: 105 times

by vikram4689 » Fri Jun 03, 2011 7:43 am

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

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

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