XimeSol
Is the size of a certain particle closer to \(10^{-3}\) centimeter than it is to \(10^{-2}\) centimeter?
(1) The size of the particle is closer to \(10^{-4}\) centimeter than it is to \(10^{-1}\) centimeter.
(2) The size of the particle is closer to \(10^{-3}\)centimeter than it is to \(10^{-1}\) centimeter.
A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
I have trouble dealing with questions such as these. So I eliminated the negative powers as much as I could.
Question: Is a number x closer to 10^-3 than it is to 10^-2?
Multiplying the equation with 10^3
Is a new number (1000x) closer to 1 than it is to 10? We can call the new number y just to simplify it further. Our new problem statement: is y closer to 1 than it is to 10?
Since we multiplied the question statement by 10^3, we will multiply the statements as well by the same number.
Statement 1: y is closer to 0.1 than it is to 100.
y could be 0.2, and the answer to the problem statement would be YES in that case.
y could be 10, and the answer would be NO.
NOT SUFFICIENT
Statement 2: y is closer to 1 than it is to 100.
y = 0.2, YES.
y = 10, NO.
NOT SUFFICIENT
Both (1) and (2) together: NOT SUFFICIENT.
Answer: E