Data Sufficiency

VJesus12 wrote:If x is an integer, is x between 27 and 54?

(1) The remainder when x is divided by 7 is 2.
(2) The remainder when x is divided by 3 is 2.

Target question: Is x between 27 and 54?

ASIDE: 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.

Statement 1: The remainder when x is divided by 7 is 2.
So, some possible values of x are: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65, . . .
As we can see, there are several values of x that satisfy statement 1. Here are two:
Case a: x = 2, in which case, the answer to the target question is NO, x is NOT between 27 and 54
Case b: x = 30, in which case, the answer to the target question is YES, x ISbetween 27 and 54
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The remainder when x is divided by 3 is 2.
So, some possible values of x are: 2, 5, 8, 11, . . . 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, . . .
As we can see, there are several values of x that satisfy statement 2. Here are two:
Case a: x = 2, in which case, the answer to the target question is NO, x is NOT between 27 and 54
Case b: x = 32, in which case, the answer to the target question is YES, x IS between 27 and 54
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x COULD equal 2, 9, 16, 23, 30, 37, 44, 51, 58, 65, . . . etc
Statement 2 tells us that x COULD equal 2, 5, 8, 11, . . . 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, . . .
There are several values of x that satisfy BOTH statements. Here are two:
Case a: x = 2, in which case, the answer to the target question is NO, x is NOT between 27 and 54
Case b: x = 44, in which case, the answer to the target question is YES, x IS between 27 and 54
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent