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What is the remainder r when x is divided by 8? x is a posit

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What is the remainder r when x is divided by 8? x is a posit [#permalink] New post 19 May 2010, 00:51
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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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Re: Remainder [#permalink] New post 19 May 2010, 01:56
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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.

Answer: C.
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Re: Remainder [#permalink] New post 19 May 2010, 02:32
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] New post 19 Feb 2014, 12:58
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Re: What is the remainder r when x is divided by 8? x is a posit [#permalink] New post 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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Re: What is the remainder r when x is divided by 8? x is a posit [#permalink] New post 07 Sep 2014, 11:48
Expert's post
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.

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 :)


1 is a factor of every integer.

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

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What is the remainder r when x is divided by 8? x is a posit   [#permalink] 07 Sep 2014, 11:48
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