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# How many 7-digit palindromes (numbers that read the same backward as f

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
How many 7-digit palindromes (numbers that read the same backward as f  [#permalink]

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28 Mar 2019, 23:48
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:44) correct 35% (02:09) wrong based on 20 sessions

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How many 7-digit palindromes (numbers that read the same backward as forward) can be formed using the digits 2, 2, 3, 3, 5, 5, 5?

(A) 6
(B) 12
(C) 24
(D) 36
(E) 48

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Intern
Joined: 12 Sep 2018
Posts: 27
Re: How many 7-digit palindromes (numbers that read the same backward as f  [#permalink]

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29 Mar 2019, 01:48
2355532
3255523

2535352
3525253

5235325
5325235

A.6
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
How many 7-digit palindromes (numbers that read the same backward as f  [#permalink]

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Updated on: 29 Mar 2019, 06:51
Bunuel wrote:
How many 7-digit palindromes (numbers that read the same backward as forward) can be formed using the digits 2, 2, 3, 3, 5, 5, 5?

(A) 6
(B) 12
(C) 24
(D) 36
(E) 48

abcdcba ; d= 5
palindrome possible
3*2*1
6
IMOA

Originally posted by Archit3110 on 29 Mar 2019, 03:30.
Last edited by Archit3110 on 29 Mar 2019, 06:51, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: How many 7-digit palindromes (numbers that read the same backward as f  [#permalink]

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29 Mar 2019, 04:05
Bunuel wrote:
How many 7-digit palindromes (numbers that read the same backward as forward) can be formed using the digits 2, 2, 3, 3, 5, 5, 5?

(A) 6
(B) 12
(C) 24
(D) 36
(E) 48

We need a 7 digit number with two 2s, two 3s and three 5s. Whatever comes in first 3 spots needs to come in the last 3 spots too so it will be in pairs. The only extra digit is a 5. Hence we will have

__ __ __ 5 __ __ __

Now, 2,3 and 5 can be arranged in the first 3 spots in 3! ways = 6 ways. Whatever the arrangement, the same arrangement will need to be maintained in the last 3 spots in reverse order e.g. 2 3 5 5 5 3 2

Hence there are only 6 ways of writing a palindrome.
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Karishma
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Re: How many 7-digit palindromes (numbers that read the same backward as f   [#permalink] 29 Mar 2019, 04:05
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