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If x is a positive integer, is (10x - 1) divisible by y

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Intern
Joined: 08 May 2014
Posts: 10
Concentration: General Management, Operations
If x is a positive integer, is (10x - 1) divisible by y  [#permalink]

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14 Nov 2014, 10:35
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Difficulty:

75% (hard)

Question Stats:

52% (01:46) correct 48% (01:48) wrong based on 88 sessions

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If x is a positive integer, is (10x - 1) divisible by y

(1) x is a multiple of y
(2) y is a prime number
Intern
Joined: 23 Oct 2012
Posts: 42
Re: If x is a positive integer, is (10x - 1) divisible by y  [#permalink]

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14 Nov 2014, 23:08
1
prakash85 wrote:
If x is a positive integer, is (10x - 1) divisible by y

(1) x is a multiple of y
(2) y is a prime number

1) x/y
x=3 , y=0.5 yes
x=4, y=2 no
insufficient

2) y is a prime number.
insufficient

1+ 2

x=4, y=2 no

x=10, y=5 no

x=20, y = 4 no

sufficient.

Thus, OA is C.
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Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 598
Re: If x is a positive integer, is (10x - 1) divisible by y  [#permalink]

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14 Nov 2014, 23:51
I would suggest that a proper GMAT question on divisibility will constrain y to be an integer. I have never seen a GMAT question that is related to factors and divisibility where a variable could be a real number.

The modified question should look like:
If x and y are positive integers, is (10x - 1) divisible by y ?

(1) x is a multiple of y
(2) y is a prime number

Cheers,
Dabral
Manager
Joined: 22 Sep 2012
Posts: 123
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: If x is a positive integer, is (10x - 1) divisible by y  [#permalink]

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15 Nov 2014, 09:00
Statement 1: x is a multiple of y
x = n* y
Now, the question becomes is 10*n*y-1 is divisible by y
Case 1: Answer is yes, if y is 1.
Case 2: Answer is no, if the y is any number other than 1 [ This is true from the theory of Co-primes i.e Two consecutive number are co-prime meaning
donot share any common factor except 1. Same holds true if one is multiple of the other ]
Therefore insufficient

Statement 2: y is a prime number
y can be 2, 3 5, 7 etc
Insufficient

Combining 1 and 2: we can say only the case 2 remains. And therefore using both statements together we can solve the problem. Answer C)
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Re: If x is a positive integer, is (10x - 1) divisible by y  [#permalink]

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27 Jan 2018, 02:43
Hello from the GMAT Club BumpBot!

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Re: If x is a positive integer, is (10x - 1) divisible by y   [#permalink] 27 Jan 2018, 02:43
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