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DS - divided by 10

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Manager
Joined: 27 Dec 2009
Posts: 167
Followers: 2

Kudos [?]: 105 [0], given: 3

DS - divided by 10 [#permalink]

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17 Jan 2010, 09:46
If x is a positive integer, is the remainder 0 when 3^x + 1 is divided by 10?
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient

What will be the correct answer ?
Senior Manager
Joined: 30 Aug 2009
Posts: 286
Location: India
Concentration: General Management
Followers: 3

Kudos [?]: 171 [1] , given: 5

Re: DS - divided by 10 [#permalink]

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17 Jan 2010, 23:59
1
KUDOS
msand wrote:
If x is a positive integer, is the remainder 0 when 3^x + 1 is divided by 10?
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient

What will be the correct answer ?

will go with A
1. 3^x has a cyclicity of 4 ie
3^1 = 3
3^2 =9
3^3 = 27[last digit 7]
3^4 = 81[last digit 1]
3^5 =243[last digit 3]

so 3^(4n+2) will be 3^6/3^10/3^14 wherein last digit will always be 9 and so 3^(4n+2) + 1 will have last digit as 0 which is divisible by 10. hence suff

stmnt 2: x>4 let x = 5 then 3^5 = 243
243 +1 = 244 not divisible by 10

let x=6 3^3 = 729
729 + 1 = 730. divisible by 10
hence not suff
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2786
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 238

Kudos [?]: 1730 [0], given: 235

Re: DS - divided by 10 [#permalink]

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18 Jan 2010, 10:12
Yes it should be A as explained above.
OA pls.
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Re: DS - divided by 10   [#permalink] 18 Jan 2010, 10:12
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DS - divided by 10

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