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19 May 2010, 01:51
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:15) correct
34%
(02:05)
wrong
based on 489
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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
(1) x yields remainder of 9 when divided by 12
(2) r is a factor of 27
19 May 2010, 02:56
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dimitri92
\(x=8q+r\), \(0\leq{r}<8\) (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.
22 Oct 2015, 11:07
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dimitri92
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
