A virus sample multiplies itself by becoming 16 times

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Source: e-GMAT

A virus sample multiplies itself by becoming 16 times 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. \(2^{25}\)

The OA is A
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by deloitte247 » Sat Aug 03, 2019 10:12 pm
Every hour, the virus increases 16 times.
Due to the anti-agent presence in the system, only 1/2 survive by 16 * 1/2 times = 8 times per hour.
Starting with x virus and after 8 hours, there are;
$$2^{40}\ virus$$
$$x\cdot8^8=2^{40}$$
$$x\cdot\left(2^3\right)^8=2^{40}$$
$$x\cdot2^{24}=2^{40}$$
$$Divide\ through\ by\ 2^{24},\ and\ apply\ the\ law\ of\ indices$$
$$We\ have,\ x=2^{40-24}=2^{16}$$

Therefore, the correct answer is option A

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by Scott@TargetTestPrep » Sun Aug 11, 2019 6:15 pm
BTGmoderatorLU wrote:Source: e-GMAT

A virus sample multiplies itself by becoming 16 times 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. \(2^{25}\)

The OA is A
If the anti-agent kills half of virus every hour, the virus only multiplies itself 8 times every hour. So if at the start, there are x number of the virus and after 8 hours, there are 2^40 viruses, we can create the equation:

x * 8^8 = 2^40

x * (2^3)^8 = 2^40

x * 2^24 = 2^40

x = 2^16

Answer: A

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