Question

If n is an integer, is $(0.1{)}^n$ greater than $(10{)}^n$?
(1) $n>-10$
(2) $n<10$

• 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.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

• will be greater than if 1 is greater than and this will be the case if and only if n < 0. Thus, we have to determine if n<0.
• From statement 1, we get that n is greater than −10. This includes non-negative values of n as well as negative values of n which is not sufficient.
• From statement 2, we get that n is less than 10, but this includes negative values of n as well as nonnegative values of n which is again not sufficient.
• Taking statements 1 and 2 together, n can have any value between −10 and 10 and can therefore be negative or nonnegative. Thus, both are insufficient.