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

Question

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

Bunuel · Accepted Answer

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.

BrentGMATPrepNow · Answer

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

dimitri92 · Answer

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

vards · Answer

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

Bunuel · Answer

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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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

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