A virus sample multiplies itself by becoming 16 time itself every hour

Question

A virus sample multiplies itself by becoming 16 time itself every hour. But due to anti-agent present in the system, only half of them survive every hour. If we start with x number of virus and after the 8 hours there are 2^40 viruses, what is the value of x?

A. 2^16
B. 2^18
C. 2^21
D. 2^23
E. 2^25

A. 2^16
B. 2^18
C. 2^21
D. 2^23
E. 2^25

chetan2u · Answer

Every hour the virus increase 16 times and then reduces to half, that is increases by 8 times or  2^3 ..
So  x*(2^3)^8=2^{40}..........x*2^{24}=2^{40}.......x=2^{40-24}=2^{16}

A

Archit3110 · Answer

every hour virus is increasing by 16 times
and due to anti agent its increase is 50% so 8 times
8 hrs virus is becoming
x*(2^3)^8 = 2^40
or say 40-24; 16
so x= 2^16
IMO A

ArindamLucky · Answer

1hr-- 2^3x
8hr -- 2^24x
Given after 8hrs value x= 2^40-16

Posted from my mobile device

ArindamLucky · Answer

1hr-- 2^3x
8hr -- 2^24x
Given after 8hrs value x= 2^40-16

Posted from my mobile device

rohailnaqvi · Answer

The virus increases 16 times every hour (or 2^4 times every hour). Half of the virus also don't survive every hour. Therefore the hourly equation becomes "(2^4)/2".
Let x be the starting point
After 8 hours the number of virus is 2^40
Therefore 2^40 = x*(2^4/2)^8
(2^4)^8 = 2^32
(2)^8 = 2^8
(2^32)/(2^8) = 2^(32-8) = 2^24

2^40 = x * 2^24
(2^40)/(2^24) = x
2(40-24) = x
2^16 = x

Answer A

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A virus sample multiplies itself by becoming 16 time itself every hour

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A virus sample multiplies itself by becoming 16 time itself every hour

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards