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# What is the remainder when the positive integer x is divided

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Intern
Joined: 20 Oct 2010
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What is the remainder when the positive integer x is divided [#permalink]

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28 Oct 2010, 21:16
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35% (medium)

Question Stats:

68% (01:10) correct 32% (01:22) wrong based on 174 sessions

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What is the remainder when the positive integer x is divided by 6?

(1) When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.
(2) When x is divided by 12, the remainder is 3.
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Re: problem from GMAT software practice test [#permalink]

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28 Oct 2010, 22:02
mybudgie wrote:
What is the best way to approach this problem? I would appreciate some help.

What is the remainder when the positive integer x is divided by 6?

Statement 1: When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.

Statement 2: When x is divided by 12, the remainder is 3.

From 1... when x is devided by 3 the reminder is zero ..so it has to be multiple of 3p
and the reminder is 1 when devided by 2 so it has to be odd.. 2(p) + 1
so when x is devided by 6 .. the reminder will be 1 ( when x is devisible of 6 when
x is devisible of 2 and 3 both )

so 1 is suffi...
Statement 2: When x is divided by 12, the remainder is 3
from when x is devided by 12 ...it has to be with 6 also...but when it carries a reminder when devided by 12... we have to think ...
since the reminder we get here < 6... it has to be the same reminder when devide with the 6 also ... so the reminder will be 3 only...
stmt 2 also suffi

so the ans : D
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Re: problem from GMAT software practice test [#permalink]

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29 Oct 2010, 00:38
mybudgie wrote:
What is the best way to approach this problem? I would appreciate some help.

What is the remainder when the positive integer x is divided by 6?

Statement 1: When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.

Statement 2: When x is divided by 12, the remainder is 3.

(1) This says that x is a multiple of 3 but not a multiple of 2.
All even multiples of 3 must be divisible by 6, and all odd multiples must be of the form 6n+3. (this is easy to see, consider the multiples - 3,6,9,12,15,18,21,... - they are alternatively even and odd, the even ones are multiples of 6 and the others sit in the middle of two multiples, hence leave remainder 3 each time divided by 6).
Sufficient

(2) x = 12k + 3 = 6(2k) + 3
Hence remainder when divided by 6 is 3
Sufficient

Answer is (d)

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Re: problem from GMAT software practice test [#permalink]

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29 Oct 2010, 03:48
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mybudgie wrote:
What is the best way to approach this problem? I would appreciate some help.

What is the remainder when the positive integer x is divided by 6?

Statement 1: When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.

Statement 2: When x is divided by 12, the remainder is 3.

This question can be very easily solved with number picking:

(1) When x is divided by 2, the remainder is 1 --> x is an odd number AND when x is divided by 3, the remainder is 0 --> x is a multiple of 3 --> so, x is an odd multiple of 3: 3, 9, 15, ... --> any such number divided by 6 yields remainder of 3. Sufficient.

(2) When x is divided by 12, the remainder is 3 --> x is of a type $$x=12q+3$$: 3, 15, 27, ... --> any such number divided by 6 yields remainder of 3. Sufficient.

Answer: D.
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Re: problem from GMAT software practice test [#permalink]

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25 Apr 2011, 18:37
For a discussion on why statement 2 is obviously sufficient, check out the following post:
http://www.veritasprep.com/blog/2011/04 ... unraveled/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Status: There is always something new !! Affiliations: PMI,QAI Global,eXampleCG Joined: 08 May 2009 Posts: 1144 Re: problem from GMAT software practice test [#permalink] ### Show Tags 25 Apr 2011, 21:25 a - multiples of 3 such as 3,9,15.Each giving remainder 3. b- 12 is a multiple of 6,giving remainder 3. Implies dividing the same number by 6 will give the remainder 3. Hence OA D. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8097 Location: Pune, India Re: problem from GMAT software practice test [#permalink] ### Show Tags 26 Apr 2011, 04:47 thangduong wrote: picking number is the fastest one. using argument is not good though MORE PROFESSIONAL. odd number which is divided by 3 is (2n+1)3, (2n+2)3 is not possible. (2n+1)3 = 6n +3 have remainder of 3 Mind you, picking numbers as a general strategy is not fool proof. Logic is. Pick numbers either as a last resort, or to get a drift of the question or when you are certain that a couple of examples will cover every scenario possible. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: problem from GMAT software practice test [#permalink]

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30 Apr 2011, 18:10
best way is by picking nos in this case

st 1 suff
no divided by 3=== 3,6,9,12,15,18,21....
also div by 2 and remainder 1 ==== 3,9,15,21
so these no when divided by 6 will always give remainder 3

st 2
no will be 12n+3 ex 3, 15,27,39,51,...
so remainder will always be 3
sufficient

hence d
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Re: problem from GMAT software practice test [#permalink]

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16 Aug 2011, 10:58
Isnt the ans B.

First stmt: no divided by 3=== 3,6,9,12,15,18,21....
also div by 2 and remainder 1 ==== 3,9,15,21
but when 3/6 gives reminder '0' and others give reminder 3. so this stmt is insufficient.

Second Stmt:
no will be 12n+3 ex 3, 15,27,39,51,...
so remainder will always be 3
sufficient

Or am i missing something ??? Please let me know
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Re: problem from GMAT software practice test [#permalink]

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16 Aug 2011, 11:14
g4gmat wrote:
Isnt the ans B.

First stmt: no divided by 3=== 3,6,9,12,15,18,21....
also div by 2 and remainder 1 ==== 3,9,15,21
but when 3/6 gives reminder '0' and others give reminder 3. so this stmt is insufficient.

Second Stmt:
no will be 12n+3 ex 3, 15,27,39,51,...
so remainder will always be 3
sufficient

Or am i missing something ??? Please let me know

3/6 gives a remainder of 3 as well. The OA is D and is correct.
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Re: What is the remainder when the positive integer x is divided [#permalink]

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03 Oct 2017, 10:26
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Re: What is the remainder when the positive integer x is divided   [#permalink] 03 Oct 2017, 10:26
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# What is the remainder when the positive integer x is divided

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