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Did the quantity of bacteria in an experiment increase by at

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Director
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Did the quantity of bacteria in an experiment increase by at [#permalink] New post 29 Oct 2012, 04:50
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

42% (01:22) correct 58% (01:12) wrong based on 19 sessions
Did the quantity of bacteria in an experiment increase by at least 15% from 1922 to 1937?

(1) The quantity of bacteria increased each year by the same percent each year from 1922 to 1937
(2) The quantity of bacteria increased by at most 1 percent each year from 1922 to 1937.

How to approach using Binomial expansion.. Q(1 + 0.01)^n
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Oct 2012, 04:54, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Did the quantity of bacteria in an experiment increase by at [#permalink] New post 29 Oct 2012, 10:28
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Here we go, just my 50 cent:
1. This one is insufficient because it says that quantity of bacteria increased each year by the same percent each year from 1922 to 1937. So it means for 15 years (or should I say 1937-1922+1=16 years, if it said including) the quantity increased by the same percent. If the same percent was 100% then we get one answer but it could be also 0.3% each year, hence 1 is out not sufficient.
2. This is more trickier, since it says by at most 1 percent each year. So we will get something similar to compound interest, i.e. Q*(1+p/100)^t=Q*1.15 or in our case Q*(1+0.01)^t>=Q*1.15 OR 1.01^t>=1.15. So we get something way out of 2-min GMAT problem, so where we have to find such t so 1.01 to the power of t would be >=1.15, It was onerous to find the values for t by regular calculation, so I used MS Excel
and go the following, as we see if t=15, then the 1.01^15>=1.15 or 1.01^15>1.15. However, the question stem 2 says that at most 1 percent, so
t 1.01^t
1 1,01
2 1,0201
3 1,030301
4 1,04060401
5 1,05101005
6 1,061520151
7 1,072135352
8 1,082856706
9 1,093685273
10 1,104622125
11 1,115668347
12 1,12682503
13 1,13809328
14 1,149474213
15 1,160968955

it could as easily interpreted not 1 percent but 0.9 percent and we would get totally different result, thus 2 is out.

Combining 1 and 2 we get that quantity of bacteria each year increased by at most 1 percent - we get one answer, but also it could be by 0.7 percent each year and we get different answer. The musings about leave us with answer (E) we need more precise details to expound upon this problem or just information provided is insufficient.
Please, correct me if I went awry

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Re: Did the quantity of bacteria in an experiment increase by at [#permalink] New post 29 Oct 2012, 13:16
Agreed normal binomial would be tasking...
(1+b)^n >= 1 +bn is helpful.
We know that the value is at least 1.15 for (1.01)^15

Other than that, I would start with 100.
yr1: 101
yr2: 102..
yr3: 103..
.
.
.
.
yr15: 115( plus some values)
At 1% max, we would get at least 15%...

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Re: Did the quantity of bacteria in an experiment increase by at   [#permalink] 29 Oct 2012, 13:16
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