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 8If x = 21, then
we get remainder 5 when we divide x by 8If x = 33 then
we get remainder 1 when we divide x by 8If 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 8Since 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 = 1Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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