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

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Math Expert
Joined: 02 Sep 2009
Posts: 44388
Medical analysts predict that one-third of all people who are infected [#permalink]

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05 Dec 2014, 07:45
Expert's post
5
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Difficulty:

55% (hard)

Question Stats:

67% (01:51) correct 33% (01:46) wrong based on 67 sessions

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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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Intern
Status: Amat Victoria Curam
Joined: 13 Sep 2014
Posts: 25
Location: India
Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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05 Dec 2014, 08:15
2
KUDOS
1
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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
Intern
Joined: 27 Oct 2014
Posts: 23
GMAT 1: 680 Q49 V34
GPA: 3.8
Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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06 Dec 2014, 02:30
1
KUDOS
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.
Manager
Joined: 04 Oct 2013
Posts: 161
Location: India
GMAT Date: 05-23-2015
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Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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06 Dec 2014, 02:32
1
KUDOS
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 = $$1-\frac{8}{27}= \frac{19}{27}$$

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Joined: 16 Oct 2010
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Location: Pune, India
Re: Medical analysts predict that one-third of all people who are infected [#permalink]

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29 Nov 2017, 02:34
2
KUDOS
Expert's post
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.

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

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01 Dec 2017, 07:50
1
KUDOS
Expert's post
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.

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Re: Medical analysts predict that one-third of all people who are infected   [#permalink] 01 Dec 2017, 07:50
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