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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