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Bunuel
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\(\frac{8.999999}{3.001} - \frac{3.999975}{1.995} =\)

A. 0.994
B. 0.996
C. 0.998
D. 1
E. 1.002

\(\frac{8.999999}{3.001} - \frac{3.999975}{1.995} =\)

\(\frac{9 - 10^{-6}}{3 + 10^{-3}} - \frac{4 - (25 * 10^{-6})}{2 - (5 * 10^{-3})} =\)

\(\frac{(3 - 10^{-3}) (3 + 10^{-3})}{(3 + 10^{-3})} - \frac{(2 + 5*10^{-3})( 2 - 5*10^{-3})}{2 - (5 * 10^{-3})} =\)

\((3 - 10^{-3}) - (2 + 5*10^{-3}) \)

\(3 - 10^{-3} - 2 - 5*10^{-3} \)

\(1 + 10^{-3} (-5 - 1) \)

\(1 - 10^{-3} (6) \)

\(1 - 0.006 \)

\(0.994\)

Option A


Could you stop here and just estimate?

\(\frac{9 - 10^{-6}}{3 + 10^{-3}} - \frac{4 - (25 * 10^{-6})}{2 - (5 * 10^{-3})} =\)

Like you know that 9/3 = 3.

Different signs in the second term means you're subtracting the result of the scientific notation, which is effectively 1 thousandth of 1, or very close to 3 ~2.999

Then for the other one, 4/2 = 2. And they're the same sign in the second term so you're adding. But you know that 25/5 means you are adding 5 thousandths or ~2.005.

Therefore, subtracting leaves .994 A
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gmatophobia
Bunuel
\(\frac{8.999999}{3.001} - \frac{3.999975}{1.995} =\)

A. 0.994
B. 0.996
C. 0.998
D. 1
E. 1.002

\(\frac{8.999999}{3.001} - \frac{3.999975}{1.995} =\)

\(\frac{9 - 10^{-6}}{3 + 10^{-3}} - \frac{4 - (25 * 10^{-6})}{2 - (5 * 10^{-3})} =\)

\(\frac{(3 - 10^{-3}) (3 + 10^{-3})}{(3 + 10^{-3})} - \frac{(2 + 5*10^{-3})( 2 - 5*10^{-3})}{2 - (5 * 10^{-3})} =\)

\((3 - 10^{-3}) - (2 + 5*10^{-3}) \)

\(3 - 10^{-3} - 2 - 5*10^{-3} \)

\(1 + 10^{-3} (-5 - 1) \)

\(1 - 10^{-3} (6) \)

\(1 - 0.006 \)

\(0.994\)

Option A


Could you stop here and just estimate?

\(\frac{9 - 10^{-6}}{3 + 10^{-3}} - \frac{4 - (25 * 10^{-6})}{2 - (5 * 10^{-3})} =\)

Like you know that 9/3 = 3.

Different signs in the second term means you're subtracting the result of the scientific notation, which is effectively 1 thousandth of 1, or very close to 3 ~2.999

Then for the other one, 4/2 = 2. And they're the same sign in the second term so you're adding. But you know that 25/5 means you are adding 5 thousandths or ~2.005.

Therefore, subtracting leaves .994 A

A test of how well this works would be trying it without knowing the answer;)

But, seriously, with answer choices this close together, you're being signaled that estimating is not a reliable substitute for an exact calculation

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