Question

What is the tens digit of positive integer x?
(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.

• 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

Answer: (A)

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

• Having a remainder of $30$ when $x$ is divided by $100$ can only happen if $x$ has a tens digit of $3$ and a ones digit of $0$, as in $130,230,630,$ and so forth; SUFFICIENT.
• When $140$ is divided by $110$, the quotient is $1$ and remainder is $30$. However, $250$ divided by $110$ yields a quotient of $2$ and remainder is $30$, and $360$ divided by $110$ gives a quotient of $3$ and remainder $30$. Since there is no consistency in the tens digit, more information is needed; NOT sufficient.
• The correct answer is A; statement 1 alone is sufficient.