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17 Jul 2019, 00:00
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D
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Difficulty:
15%
(low)
Question Stats:
81% (01:27) correct
19%
(02:12)
wrong
based on 52
sessions
History
Date
Time
Result
Not Attempted Yet
If one-third of the water is removed with each stroke of drainage pump, what fraction of the original amount is left after 4 strokes?
(A) \(\frac{1}{27}\)
(B) \(\frac{4}{9}\)
(C) \(\frac{8}{27}\)
(D) \(\frac{16}{81}\)
(E) \(\frac{16}{243}\)
(A) \(\frac{1}{27}\)
(B) \(\frac{4}{9}\)
(C) \(\frac{8}{27}\)
(D) \(\frac{16}{81}\)
(E) \(\frac{16}{243}\)
17 Jul 2019, 00:11
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Didn't solve but found something to answer quickly.
Since 1/3rd amount is removed in one stroke 4 strokes would leave a fraction with denominator of 3^4.
Only D has that. Hence Answer (D)
Since 1/3rd amount is removed in one stroke 4 strokes would leave a fraction with denominator of 3^4.
Only D has that. Hence Answer (D)
17 Jul 2019, 00:20
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Bunuel
If one-third of the water is removed with each stroke of drainage pump, what fraction of the original amount is left after 4 strokes?
(A) \(\frac{1}{27}\)
(B) \(\frac{4}{9}\)
(C) \(\frac{8}{27}\)
(D) \(\frac{16}{81}\)
(E) \(\frac{16}{243}\)
(A) \(\frac{1}{27}\)
(B) \(\frac{4}{9}\)
(C) \(\frac{8}{27}\)
(D) \(\frac{16}{81}\)
(E) \(\frac{16}{243}\)
Fraction of water left after 1st stroke \(= 1-\frac{1}{4} = \frac{2}{3}\)
Fraction of water left after 2nd stroke \(= \frac{2}{3} * \frac{2}{3} = \frac{2^2}{3^2}\)
Fraction of water left after 3rd stroke \(= \frac{2}{3} * \frac{2^2}{3^2} = \frac{2^3}{3^3}\)
Fraction of water left after 4th stroke \(= \frac{2}{3} * \frac{2^3}{3^3} = \frac{2^4}{3^4} = \frac{16}{81}\)
IMO D
