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

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Question Stats: 66% (02:18) correct 34% (02:04) wrong based on 378 sessions

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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
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Joined: 02 Sep 2009
Posts: 58452

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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.

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hmm ..i missed this part of finding the remainder in 1 ...hope i dont repeat this mistake on GMAT
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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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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.

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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Math Expert V
Joined: 02 Sep 2009
Posts: 58452
Re: What is the remainder r when x is divided by 8? x is a posit  [#permalink]

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vards wrote:
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.

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 1 is a factor of every integer.

Check for more here: divisibility-multiples-factors-tips-and-hints-174998.html

Hope it helps.
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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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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

Cheers,
Brent
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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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_________________ Re: What is the remainder r when x is divided by 8? x is a posit   [#permalink] 10 Aug 2018, 20:44
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