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GRE Quantitative Reasoning QUESTION #8069
Question 1

$d = 5.03894$ and $\overline{d}$ is the decimal expression for $d$ rounded to the nearest thousandth.

Compare:

Column A: The number of decimal places where $d$ and $\overline{d}$ differ

Column B: 4

  • Column A is greater
  • Column B is greater✔️
  • The two quantities are equal
  • The relationship cannot be determined
Correct Answer Explanation

When we round $d = 5.03894$ to the nearest thousandth, we get $\overline{d} = 5.039$ (since the fourth decimal place is 9, which is $\geq 5$, we round up).

Comparing digit by digit:

  • Position 1 (units): both have 5 ✓
  • Position 2 (tenths): both have 0 ✓
  • Position 3 (hundredths): both have 3 ✓
  • Position 4 (thousandths): $d$ has 8, $\overline{d}$ has 9 ✗
  • Position 5 onwards: $d$ has 94, $\overline{d}$ has nothing

The positions where they differ are the thousandths place and beyond (positions 4, 5, 6...). If we count decimal places where values differ, we get 3 places (the thousandth, ten-thousandth, and hundred-thousandth positions).

Actually, re-reading: the question asks for decimal PLACES where they differ. Since $\overline{d}$ ends at thousandths, comparing through all decimal places in $d$: they differ at the 4th and 5th decimal positions. That's 2 places, which is less than 4.

Therefore Column B is greater.