At a lab, bacteria P multiplies itself in every 18 days, while bacteri

Bunuel

Can you please confirm-Even I got the answer as C 20%

=73-61/61=20%
Where, Q multiplies 73 times and P 61 times.

At a lab, bacteria P multiplies itself in every 18 days, while bacteria Q multiplies itself in every 15 days. Approximately by what percent is the number of times bacteria Q multiplies itself is more than the number of times bacteria P multiplies itself in a 3-year period?

(A) 12%
(B) 16%
(C) 20%
(D) 22%
(E) 33%

At a lab, bacteria P multiplies itself in every 18 days, while bacteria Q multiplies itself in every 15 days. Approximately by what percent is the number of times bacteria Q multiplies itself is more than the number of times bacteria P multiplies itself in a 3-year period?

(A) 12%
(B) 16%
(C) 20%
(D) 22%
(E) 33%

Let, Total days = LCM (15 and 18) = 90

P multiplies 90/18 = 5 times in 90 days
Q multiplies 90/15 = 6 times in 90 days

i.e. in any given time (i.e. 3 years as well) the number of times bacteria Q multiplies itself is more than the number of times bacteria P multiplies itself = (6-5)*100/5 = 20%

Answer: Option C

 

The assumption above in red is absolutely not warranted, the cyclicity GMATinsight claimed will only be true when the number of days (d) falls within the range \( 90*k - 15 < d < 90*k + 15 \), where k is a positive integer (i.e. k= 1, 2, 3, ....). Outside this range, the distribution of the no. of cycles of P to that of Q will not be in the ratio 5:6 because either Q would not have completed its final cycle or would have completed its cycle earlier than P (I know this sounds overcomplicated, but I lack the comm to make it any simpler than this. When you read the explanation with the example below you'll get what I am saying) 

Imagine we are on the day 105, P would have completed 105/18 = 5 cycles, BUT Q would have completed 105/15 = 7 cycles (Note that d = 105 is of the form 90*1 + 15 which falls outside the range that we found above, and hence, the cycles are uneven i.e. not in the ration 5:6)

Now coming to our problem, since 3 years have 365*3 = 1095 days which is 90*12 + 15, it falls juusst outside of the range we found above hence the cycles will not be a normal 5:6 ratio cycle (if you do the calculation by hand you'll see P undergoes 60 complete cycles (1095/18) whereas Q undergoes 73 complete cycles (1095/15) AND NOT 60*(6/5) i.e. 72, and hence, the answer turns out to be \(\frac{73-60}{60}*100\)­ => 1300/60 ≅ 21.67% closer to 22%. CHOICE D is correct.

Nice test of LCM and uneven cycles in the question.

I hope this helps someone.­

Q doubles 73 times in 3 years.

P doubles 60 5/6 times over the same period.

Truncating 60 5/6 to 60 is the difference between 20% and 22%.

Since the question doesn't clearly stipulate that it is interested in the number of "complete" doublings, the normal understanding that bacterial growth is a continuous process should prevail, with 60 5/6 and 20% being the appropriate answer.

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   the normal understanding that bacterial growth is a continuous process should prevail, with 60 5/6 and 20% being the appropriate answer.

Since the question doesn't clearly stipulate that it is interested in the number of "complete" doublings,

At a lab, bacteria P multiplies itself in every 18 days, while bacteria Q multiplies itself in every 15 days. Approximately by what percent is the number of times bacteria Q multiplies itself is more than the number of times bacteria P multiplies itself in a 3-year period?

(A) 12%
(B) 16%
(C) 20%
(D) 22%
(E) 33%

Bacteria P multiplies itself in every 18 days =>
at 0 days = x number of bacteria P
after 18 days = 2x
after 36 days = 2* (2x) = 4x
after 56 days = 2*(4x) = 2^(56/18) times of x = 2^3 times of x
...
after 3 yrs = 2^(365*3/18) times of x= 2^(60.83) times of x ......(bacteria P)

Similarly, bacteria Q multiplies itself in every 15 days =>
at 0 days = y number of bacteria Q
after 3 yrs = 2^(365*3/15) times of y = 2^73 times of y .......(bacteria Q)

Here the number of times the bacteria increases is exponential not linear. Which will give different answer.

Can some pls explain?


Bunuel GMATinsight

Bacteria P multiplies itself in every 18 days =>
at 0 days = x number of bacteria P
after 18 days = 2x
after 36 days = 2* (2x) = 4x
after 56 days = 2*(4x) = 2^(56/18) times of x = 2^3 times of x
...
after 3 yrs = 2^(365*3/18) times of x= 2^(60.83) times of x ......(bacteria P)

Similarly, bacteria Q multiplies itself in every 15 days =>
at 0 days = y number of bacteria Q
after 3 yrs = 2^(365*3/15) times of y = 2^73 times of y .......(bacteria Q)

Here the number of times the bacteria increases is exponential not linear. Which will give different answer.

Can some pls explain?


Bunuel GMATinsight