Question

$d=0.43t7$
If t denotes the thousandths digit in the decimal representation of d above, what digit is t?
(1) If d were rounded to the nearest hundredth, the result would be 0.44.
(2) If d were rounded to the nearest thousandth, the result would be 0.436.

• 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: (B)

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

We have to determine $t$, the thousandths digit of $d=0.43t7.$

1. Since d rounded to the nearest hundredth is $0.44$, $t$ can be $5,6,7,8,or9$ because each of $0.4357,0.4367,0.4377,0.4387,$ and $0.4397$ rounded to the nearest hundredth is $0.44$; NOT sufficient.
2. Since $d$ rounded to the nearest thousandth is $0.436$ and the digit in ten-thousandths place of $d$ is $7$, the digit in thousandths place gets increased by $1$ in the rounding process. Thus, $t+1=6$ and $t=5.$ Thus, this is sufficient. The correct answer is B; statement 2 alone is sufficient.