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What is the Remainder R when X is divided by 8? X is a positive integer.

(1) X yields 9 when divided by 12 (2) R is a factor of 27

\(x=8q+r\), \(0\leq{r}<8\) (remainder must be less than divisor). Question \(r=?\).

(1) Think this statement should be: "x yields remainder of 9 when divided by 12" --> \(x=12p+9\), \(x\) can take following values: 9, 21, 33, 45, 57, ... This values divided by 8 can give remainder of 1 or 5. Two values. Not sufficient.

(2) \(rk=27\), as \(0\leq{r}<8\), then r can take only two values: 1 or 3. Two values. Not sufficient.

(1)+(2) Intersection of values from (1) and (2) is \(r=1\). Sufficient.

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19 Feb 2014, 12:58

Hello from the GMAT Club BumpBot!

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Re: What is the remainder r when x is divided by 8? x is a posit [#permalink]

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07 Sep 2014, 11:38

Bunuel wrote:

dimitri92 wrote:

What is the Remainder R when X is divided by 8? X is a positive integer.

(1) X yields 9 when divided by 12 (2) R is a factor of 27

\(x=8q+r\), \(0\leq{r}<8\) (remainder must be less than divisor). Question \(r=?\).

(1) Think this statement should be: "x yields remainder of 9 when divided by 12" --> \(x=12p+9\), \(x\) can take following values: 9, 21, 33, 45, 57, ... This values divided by 8 can give remainder of 1 or 5. Two values. Not sufficient.

(2) \(rk=27\), as \(0\leq{r}<8\), then r can take only two values: 1 or 3. Two values. Not sufficient.

(1)+(2) Intersection of values from (1) and (2) is \(r=1\). Sufficient.

Answer: C.

Hi Bunuel, need ur help buddy.. Actually,when i came at the end of this problem, i had 3 and 9 as factors of 27..But,as it was given,the remainder is a factor of 27..so it only has to be 3,since 9 is greater than 8..i understand that when we divide9 by 8,we get 1 as remainder,but we are explicitly told that remainder is a factor of 27 and 1 is not a factor,so we are left with just 3.. please clear my understanding..thanks
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What is the Remainder R when X is divided by 8? X is a positive integer.

(1) X yields 9 when divided by 12 (2) R is a factor of 27

\(x=8q+r\), \(0\leq{r}<8\) (remainder must be less than divisor). Question \(r=?\).

(1) Think this statement should be: "x yields remainder of 9 when divided by 12" --> \(x=12p+9\), \(x\) can take following values: 9, 21, 33, 45, 57, ... This values divided by 8 can give remainder of 1 or 5. Two values. Not sufficient.

(2) \(rk=27\), as \(0\leq{r}<8\), then r can take only two values: 1 or 3. Two values. Not sufficient.

(1)+(2) Intersection of values from (1) and (2) is \(r=1\). Sufficient.

Answer: C.

Hi Bunuel, need ur help buddy.. Actually,when i came at the end of this problem, i had 3 and 9 as factors of 27..But,as it was given,the remainder is a factor of 27..so it only has to be 3,since 9 is greater than 8..i understand that when we divide9 by 8,we get 1 as remainder,but we are explicitly told that remainder is a factor of 27 and 1 is not a factor,so we are left with just 3.. please clear my understanding..thanks

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22 Oct 2015, 07:08

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the remainder r when x is divided by 8? x is a posit [#permalink]

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22 Oct 2015, 10:07

2

This post received KUDOS

dimitri92 wrote:

What is the remainder r when x is divided by 8? x is a positive integer.

(1) x yields remainder of 9 when divided by 12 (2) r is a factor of 27

When it comes to remainders, we have a nice rule that says: If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Now onto the question...............

Target question:What is the remainder r when x is divided by 8?

Statement 1: x yields remainder of 9 when divided by 12 By the rule above, the possible values of x are: 9, 21, 33, 45, 57, 69,.... Let's check out the remainder when we divide these possible x-values by 8 If x = 9, then we get remainder 1 when we divide x by 8 If x = 21, then we get remainder 5 when we divide x by 8 If x = 33 then we get remainder 1 when we divide x by 8 If x = 45, then we get remainder 5 when we divide x by 8 . . . Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: r is a factor of 27 We have no information about the value of x, so there's no way to determine the remainder when x is divided by 8 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that remainder r is EITHER 1 OR 5 Statement 2 tells us that r is a factor of 27 Since only 1 is a factor of 27, we can be certain that remainder r = 1 Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers, Brent
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Brent Hanneson – Founder of gmatprepnow.com

Brent also tutors students for the GMAT

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Re: What is the remainder r when x is divided by 8? x is a posit
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22 Oct 2015, 10:07

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