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Medical analysts predict that one-third of all people who are infected

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Medical analysts predict that one-third of all people who are infected [#permalink]

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Tough and Tricky questions: Probability.



Medical analysts predict that one-third of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?

A) 16/81
B) 8/27
C) 2/3
D) 19/27
E) 65/81

Kudos for a correct solution.

Source: Chili Hot GMAT
[Reveal] Spoiler: OA

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Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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New post 05 Dec 2014, 07:15
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at the end of day 1 - Dead = 1/3, alive = 1 - 1/3 = 2/3
at the end of day 2 - Dead = 1/3 + (1/3).(2/3), alive = 1 - {1/3 + (1/3).(2/3)} = 4/9
at the end of day 3 - Dead = 1/3 + (1/3).(2/3) + (1/3).(4/9) = 19/27

Hence D

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Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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New post 06 Dec 2014, 01:30
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At the end of each day we will have 2/3 alive. So after 3 days we will have (2/3)^3 people alive. Therefore, fraction of dead people will be 1-(2/3)^3=19/27.
The correct answer is D.

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Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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Medical analysts predict that one-third of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?

A) 16/81
B) 8/27
C) 2/3
D) 19/27
E) 65/81


People expected to be killed at the end of first day = \(1000*(\frac{1}{3})\)
Remaining people, expected not to be killed at the end of first day= \(1000*(\frac{2}{3})\)

People expected to be killed at the end of second day = \(1000*(\frac{2}{3})(\frac{1}{3})\)
Remaining people, expected not to be killed at the end of second day= \(1000*(\frac{2}{3})^2\)

One may observe that the number of people expected as not killed follows a geometric progression with initial value as 1000 and fixed common ratio (\(\frac{2}{3}\)). Thus, people expected not to be killed at the end of third day = \(1000*(\frac{2}{3})^3 = (\frac{8}{27})*1000\)

Therefore, fraction of 1,000 people that could be expected to be killed in three full days = \(1-\frac{8}{27}= \frac{19}{27}\)

Answer: D

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Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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New post 29 Nov 2017, 01:34
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Bunuel wrote:

Tough and Tricky questions: Probability.



Medical analysts predict that one-third of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?

A) 16/81
B) 8/27
C) 2/3
D) 19/27
E) 65/81

Kudos for a correct solution.

Source: Chili Hot GMAT


Since we need the answer in fraction, we can ignore the 1000.

At the end of every day, 2/3rd of the previous day's number is left.

So at the end of day three, (2/3)*(2/3)*(2/3) = 8/27 are left

So by the end of day three, 1 - 8/27 = 19/27 could be expected to be killed.

Answer (D)
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Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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New post 01 Dec 2017, 06:50
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Bunuel wrote:

Tough and Tricky questions: Probability.



Medical analysts predict that one-third of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote. What fraction of a group of 1,000 people could be expected to be killed if infected and not treated for three full days?

A) 16/81
B) 8/27
C) 2/3
D) 19/27
E) 65/81


Instead of using 1,000, let’s use variable t.

After day 1, (1/3)t have not survived and (2/3)t are left.

After day 2, (2/3)t x 1/3 = (2/9)t have not survived and (2/3)t x 2/3 = (4/9)t are left.

After day 3, (4/9)t x 1/3 = (4/27)t have not survived and (4/9)t x 2/3 = (8/27)t are left.

Thus, after 3 days the fraction that have not survived is (1/3)t + (2/9)t + (4/27)t = (9/27)t + (6/27)t + (4/27)t = (19/27)t.

Answer: D
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Kudos [?]: 1019 [1], given: 3

Re: Medical analysts predict that one-third of all people who are infected   [#permalink] 01 Dec 2017, 06:50
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