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10 Feb 2023, 15:19
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
51% (02:12) correct
49%
(01:53)
wrong
based on 501
sessions
History
Date
Time
Result
Not Attempted Yet
\(\frac{8.999999}{3.001} - \frac{3.999975}{1.995} =\)
A. 0.994
B. 0.996
C. 0.998
D. 1
E. 1.002
A. 0.994
B. 0.996
C. 0.998
D. 1
E. 1.002
11 Feb 2023, 23:52
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Bunuel
\(\frac{8.999999}{3.001} - \frac{3.999975}{1.995} =\)
\(\frac{9 - 10^{-6}}{3 + 10^{-3}} - \frac{4 - (25 * 10^{-6})}{2 - (5 * 10^{-3})} =\)
\(\frac{(3 - 10^{-3}) (3 + 10^{-3})}{(3 + 10^{-3})} - \frac{(2 + 5*10^{-3})( 2 - 5*10^{-3})}{2 - (5 * 10^{-3})} =\)
\((3 - 10^{-3}) - (2 + 5*10^{-3}) \)
\(3 - 10^{-3} - 2 - 5*10^{-3} \)
\(1 + 10^{-3} (-5 - 1) \)
\(1 - 10^{-3} (6) \)
\(1 - 0.006 \)
\(0.994\)
Option A
General Discussion
15 Feb 2023, 19:38
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gmatophobia
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
