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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1435
Location: India
A positive integer N is a six digit number of the form  [#permalink]

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4 00:00

Difficulty:   75% (hard)

Question Stats: 56% (02:37) correct 44% (02:44) wrong based on 64 sessions

### HideShow timer Statistics A positive integer N is a six digit number of the form xyxyyy where x and y are distinct digits. What is the value of x?

(1) N is divisible by 6.

(2) N is divisible by each integer from 1 to 5.

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Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: A positive integer N is a six digit number of the form  [#permalink]

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2
1
A positive integer N is a six digit number of the form xyxyyy where x and y are distinct digits. What is the value of x?

(1) N is divisible by 6.
just tells us that x+y+x+y+y+y+y is divisible by 3 and y is even
so 2(x+2y) is div by 3
x can be 3 and y = 0
x can be 5, and y = 2
insuff

(2) N is divisible by each integer from 1 to 5.
this means y is multiple of 5, hence 0 or 5
x can be anything
insuff

combined
y=0, x can be 3 and nunmber 303000
also y=0, x=6 0r 9
insuff

e
_________________
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Joined: 18 Apr 2018
Posts: 93
Re: A positive integer N is a six digit number of the form  [#permalink]

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chetan2u wrote:
A positive integer N is a six digit number of the form xyxyyy where x and y are distinct digits. What is the value of x?

(1) N is divisible by 6.
just tells us that x+y+x+y+y+y+y is divisible by 3 and y is even
so 2(x+2y) is div by 3
x can be 3 and y = 0
x can be 5, and y = 2
insuff

(2) N is divisible by each integer from 1 to 5.
this means y is multiple of 5, hence 0 or 5
x can be anything
insuff

combined
y=0, x can be 3 and nunmber 303000
also y=0, x=6 0r 9
insuff

e

Hello, I have a question about statement 2.

(2) N is divisible by each integer from 1 to 5.

Doesn't this means that N is divisible by 1,2,3,4 and 5? If so, doesn't this statement mean that N is divisible by 2 and 3 as well as 5 and makes y=0 and x=3 making option C sufficient? Thanks.
chetan2u

Posted from my mobile device
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: A positive integer N is a six digit number of the form  [#permalink]

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1
Kem12 wrote:
chetan2u wrote:
A positive integer N is a six digit number of the form xyxyyy where x and y are distinct digits. What is the value of x?

(1) N is divisible by 6.
just tells us that x+y+x+y+y+y+y is divisible by 3 and y is even
so 2(x+2y) is div by 3
x can be 3 and y = 0
x can be 5, and y = 2
insuff

(2) N is divisible by each integer from 1 to 5.
this means y is multiple of 5, hence 0 or 5
x can be anything
insuff

combined
y=0, x can be 3 and nunmber 303000
also y=0, x=6 0r 9
insuff

e

Hello, I have a question about statement 2.

(2) N is divisible by each integer from 1 to 5.

Doesn't this means that N is divisible by 1,2,3,4 and 5? If so, doesn't this statement mean that N is divisible by 2 and 3 as well as 5 and makes y=0 and x=3 making option C sufficient? Thanks.
chetan2u

Posted from my mobile device

Hi..
Number is xyxyyy .
Div by 1 to 5 means div by LCM of 1,2,3,4,5, =60 so Ans can be 303000 or 606000 or 909000
So X could be 3, or 6, or 9
Insuff
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Manager  B
Joined: 18 Apr 2018
Posts: 93
Re: A positive integer N is a six digit number of the form  [#permalink]

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Thanks @chetan2u...understood.

Posted from my mobile device
Intern  B
Joined: 24 Mar 2015
Posts: 26
Re: A positive integer N is a six digit number of the form  [#permalink]

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chetan2u wrote:
A positive integer N is a six digit number of the form xyxyyy where x and y are distinct digits. What is the value of x?

(1) N is divisible by 6.
just tells us that x+y+x+y+y+y+y is divisible by 3 and y is even
so 2(x+2y) is div by 3
x can be 3 and y = 0
x can be 5, and y = 2
insuff

(2) N is divisible by each integer from 1 to 5.
this means y is multiple of 5, hence 0 or 5
x can be anything
insuff

combined
y=0, x can be 3 and nunmber 303000
also y=0, x=6 0r 9
insuff

e

Hi,
for the reason of {2}, i guess , i am missing something please correct me if needed.

N is divisible by each integer from 1 to 5.
this means y is multiple of 5, hence 0 or 5

1,2,3,4,5 are all factors of the number xyxyyy

for 5 divisibility the last digit need to be 0 or 5. But for 4 divisibility it need to be last two digits must be divisible by 4 so cannot be ( 55 ), but 00 (yes).
for 3 divisibility sum should be multiple of 3k ie x can be 3,6,9
x= 3,6,9 y=0.

right.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1435
Location: India
Re: A positive integer N is a six digit number of the form  [#permalink]

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Tamao411284 wrote:
chetan2u wrote:
A positive integer N is a six digit number of the form xyxyyy where x and y are distinct digits. What is the value of x?

(1) N is divisible by 6.
just tells us that x+y+x+y+y+y+y is divisible by 3 and y is even
so 2(x+2y) is div by 3
x can be 3 and y = 0
x can be 5, and y = 2
insuff

(2) N is divisible by each integer from 1 to 5.
this means y is multiple of 5, hence 0 or 5
x can be anything
insuff

combined
y=0, x can be 3 and nunmber 303000
also y=0, x=6 0r 9
insuff

e

Hi,
for the reason of {2}, i guess , i am missing something please correct me if needed.

N is divisible by each integer from 1 to 5.
this means y is multiple of 5, hence 0 or 5

1,2,3,4,5 are all factors of the number xyxyyy

for 5 divisibility the last digit need to be 0 or 5. But for 4 divisibility it need to be last two digits must be divisible by 4 so cannot be ( 55 ), but 00 (yes).
for 3 divisibility sum should be multiple of 3k ie x can be 3,6,9
x= 3,6,9 y=0.

right.

Hello

I think your analysis is correct. Since from second statement we get y=0 but there is no unique value of x, hence second statement is not sufficient. Re: A positive integer N is a six digit number of the form   [#permalink] 16 Aug 2018, 10:42
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# A positive integer N is a six digit number of the form  