GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 08 Dec 2019, 00:54 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A strain of bacteria multiplies such that the ratio of its p

Author Message
TAGS:

### Hide Tags

Manager  Joined: 09 Dec 2009
Posts: 116
A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

2
22 00:00

Difficulty:

(N/A)

Question Stats: 71% (00:30) correct 29% (06:00) wrong based on 40 sessions

### HideShow timer Statistics

A strain of bacteria multiplies such that the ratio of its population in any two consecutive minutes is constant. If the bacteria grows from a a population of 5 million to 40 million over the course on an hour, by what factor does the population increase every 10 minutes?

$$\sqrt{2}$$
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

2
4
taleesh wrote:
Can somebody please show the understandable solution to this question, I appreciate the above mention solutions by Maths prodigies( which isn't me) but i need a simple solution to this question that can be implemented in the time constraint of Gmat.

If geometric progression is applied here - what is the common ratio?

A strain of bacteria multiplies such that the ratio of its population in any two consecutive minutes is constant. If the bacteria grows from a a population of 5 million to 40 million over the course on an hour, by what factor does the population increase every 10 minutes?

In 60 minutes the population increased 8 times. So, if the growth rate per minute is r, then $$r^{60}=8=2^3$$. The question asks what factor the population will grow by in 10 minutes. The growth rate in 10 minutes is $$r^{10}$$. take 6th root from $$r^{60}=2^3$$ --> $$r^{10}=\sqrt{(2^3)}=\sqrt{2}$$

Hope it's clear.
_________________
SVP  Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2478
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

5
2
Consider the values of bacteria as a sequence.
Since ratio of consecutive terms is constant , this is geometric progression.

with 1st term as a =5 , last term as $$ar^{60} = 40$$

=>$$r^{60}= 8$$ => $$r^{20}$$ = 2
=> $$r^{10}$$ = $$\sqrt{2}$$

we need to find the factor after 10 mins
which is $$r^{10}$$
= $$\sqrt{2}$$
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Originally posted by gurpreetsingh on 20 Feb 2010, 00:46.
Last edited by gurpreetsingh on 20 Feb 2010, 10:11, edited 1 time in total.
##### General Discussion
SVP  Joined: 29 Aug 2007
Posts: 1804
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

1
1
Currency wrote:
A strain of bacteria multiplies such that the ratio of its population in any two consecutive minutes is constant. If the bacteria grows from a a population of 5 million to 40 million over the course on an hour, by what factor does the population increase every 10 minutes?

\sqrt{2}

These linear and geometric sequences ar rattling me. Can anyone take a run at explaining the answer here?

Thanks

c

Interval = 10 minuets
1 hour = 60 min/10 min = 6 intervals

5 mil (1+x)^6 = 40 mil where (1 + x) is the rate of change (constant ratio).
(1+x)^6 = 8
(1+x)^6 = (sqrt 2)^6
1 + x = sqrt 2

1 + x is the rate of change (constant ratio). So its sqrt 2.
Manager  Joined: 09 Dec 2009
Posts: 116
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

gurpreetsingh wrote:
with 1st term as a =5 , last term as

=> =>
=> =

we need to find the factor after 10 mins
which is
=

can you break it down further? Can you put the formula used and define each term? Cutting right to plugging in is moving too fast for me on this questions.

Also where did the 0 come from in your answer, and why did it just disappear when it looked like it should have made the whole side of that equation zero.

Thanks
SVP  Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2478
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

1
There is no zero, its actually r raised to the power 60, 20 and 10...its not coming in alignment.
( Mods pls correct it if I m doing something wrong)

geometric progression has terms as : a , ar , $$ar^2$$ ..... $$ar^(n-1)$$
In Gp series, ratio of consecutive terms is constant.

Since its given that ratio of population of consecutive terms is constant, that means we can consider the values of population as terms of Gp series... with initial term a = 5

after 1 min it will be ar
after 2 min it will be ar^2
.................................
after 10 min it will be ar^10
.................................
after 60 min it will be ar^60 = 40
now just use the value of "a' here and find r^10 which is the population after 10 mins.
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html
Manager  Joined: 18 Feb 2010
Posts: 126
Schools: ISB
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

TheSituation wrote:
A strain of bacteria multiplies such that the ratio of its population in any two consecutive minutes is constant. If the bacteria grows from a a population of 5 million to 40 million over the course on an hour, by what factor does the population increase every 10 minutes?

\sqrt{2}

These linear and geometric sequences ar rattling me. Can anyone take a run at explaining the answer here?

Thanks

c

Since the series you know is a geometric one we have to solve like this...

let the series be 5, a1, a2, a3, a4, a5 , 40

where a1 is population after 10 minutes
a2 after 20 and so on....
40 is the population at 60th minute.

We need to find the ratio of increase which is driven by a formula (40/5)^(1/6)

here 40 is last term
5 is first term
6 comes from 5 intervals + 1

so we get sqrt2...

Hope it helps
Intern  Joined: 29 Oct 2009
Posts: 30
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

1
Series will be 5 5x 5x^2 5x^3----5x^10--------5x^60

X^10 we need to find out.

So
5x^60 = 40
X^60 = 8
((X^10)^2)^3 = 8
X^10 = 2^(1/2)
Manager  Joined: 06 Mar 2014
Posts: 220
Location: India
GMAT Date: 04-30-2015
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

Yet to find a more apt explanation to it.

My take on it: p - population

t=0, p = 5 mil

t= 60 minutes, p = 40 mil

let r be the rate of increase.

at t=1, we have pr
t =2, pr^2 (where p is the initial population - 5)

hence, t=60,
40 = 5*r^60
--> r^60 = 8
Since we are look for r at every 10 minutes, we can take the sixth root both sides
r^10 = 2^0.5
Intern  Joined: 18 Jul 2013
Posts: 31
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

1
Can somebody please show the understandable solution to this question, I appreciate the above mention solutions by Maths prodigies( which isn't me) but i need a simple solution to this question that can be implemented in the time constraint of Gmat.

If geometric progression is applied here - what is the common ratio?
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

4
Bacteria.................. Start

5 ................................ 0

5x .............................. 10 Minutes (Say x is the multiplication factor)

$$5x^2$$ ........................... 20 Minutes

$$5x^3$$ ........................... 30 Minutes

$$5x^4$$ ........................... 40 Minutes

$$5x^5$$ ........................... 50 Minutes

$$5x^6$$ ........................... 60 Minutes

Given that $$5x^6 = 40$$

$$x^6 = 8 = 2^3$$

$$x = 2^{\frac{3}{6}} = \sqrt{2}$$
Manager  Joined: 02 Jul 2012
Posts: 183
Location: India
Schools: IIMC (A)
GMAT 1: 720 Q50 V38 GPA: 2.6
WE: Information Technology (Consulting)
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

1
Someone please correct me in the following procedure

5X^6 = 40
X^6 = 8
X^6 = 2^3
X^3 = 2
X = (2)^1/3

What's wrong with the above procedure ?
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

1
Thoughtosphere wrote:
Someone please correct me in the following procedure

5X^6 = 40
X^6 = 8
X^6 = 2^3
X^3 = 2
X = (2)^1/3

What's wrong with the above procedure ?

When taking the cube root from $$x^6 = 2^3$$, we get $$(x^6)^{(\frac{1}{3})} = (2^3)^{(\frac{1}{3})}$$ --> $$x^2 = 2$$ --> $$x = \sqrt{2}$$.

Hope it helps.
_________________
Manager  Joined: 02 Jul 2012
Posts: 183
Location: India
Schools: IIMC (A)
GMAT 1: 720 Q50 V38 GPA: 2.6
WE: Information Technology (Consulting)
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

Bunuel wrote:
Thoughtosphere wrote:
Someone please correct me in the following procedure

5X^6 = 40
X^6 = 8
X^6 = 2^3
X^3 = 2
X = (2)^1/3

What's wrong with the above procedure ?

When taking the cube root from $$x^6 = 2^3$$, we get $$(x^6)^{(\frac{1}{3})} = (2^3)^{(\frac{1}{3})}$$ --> $$x^2 = 2$$ --> $$x = \sqrt{2}$$.

Hope it helps.

Bang On!!!!

Thanks a lot... +1 to you... Intern  Joined: 18 Jul 2013
Posts: 31
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

Thanks a lot Bunnel and Paresh.
Senior Manager  B
Joined: 10 Mar 2013
Posts: 461
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A\$)
GMAT 1: 580 Q46 V24 GPA: 3.88
WE: Information Technology (Consulting)
A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

This question gives us more information than we need... in 1 hour (60 min) population grows by factor 8... so it doubles every 20 min --> k^20 = 2 --> k^20/2 or k^10 = 2^1/2

Alternative
K^60 = 8 (40 Mio / 5 Mio) --> k^10 = 8^1/6 = 2^1/2
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

Bunuel wrote:
taleesh wrote:
Can somebody please show the understandable solution to this question, I appreciate the above mention solutions by Maths prodigies( which isn't me) but i need a simple solution to this question that can be implemented in the time constraint of Gmat.

If geometric progression is applied here - what is the common ratio?

A strain of bacteria multiplies such that the ratio of its population in any two consecutive minutes is constant. If the bacteria grows from a a population of 5 million to 40 million over the course on an hour, by what factor does the population increase every 10 minutes?

In 60 minutes the population increased 8 times. So, if the growth rate per minute is r, then $$r^{60}=8=2^3$$. The question asks what factor the population will grow by in 10 minutes. The growth rate in 10 minutes is $$r^{10}$$. take 6th root from $$r^{60}=2^3$$ --> $$r^{10}=\sqrt{(2^3)}=\sqrt{2}$$

Hope it's clear.

Similar questions to practice:
it-takes-30-days-to-fill-a-laboratory-dish-with-bacteria-140269.html
if-a-certain-culture-of-bacteria-increases-by-a-constant-158863.html
a-certain-bacteria-colony-doubles-in-size-every-day-for-144013.html
a-strain-of-bacteria-multiplies-such-that-the-ratio-of-its-p-90600.html
the-population-of-locusts-in-a-certain-swarm-doubles-every-90353.html
the-number-of-water-lilies-on-a-certain-lake-doubles-every-142858.html
during-an-experiment-the-growth-rate-of-a-bacteria-colony-177023.html
the-population-of-a-bacteria-culture-doubles-every-2-minutes-167378.html
wes-works-at-a-science-lab-that-conducts-experiments-on-bacteria-the-186310.html
a-certain-population-of-bacteria-doubles-every-10-minutes-if-the-numb-189467.html
the-population-of-growthtown-doubles-every-50-years-if-the-number-of-191456.html
the-population-of-a-bacteria-colony-doubles-every-day-if-it-was-start-114673.html
_________________
Manager  B
Joined: 27 Mar 2017
Posts: 97
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

I have 1 very basic confusion. Since the interval is 60 minutes, shouldn't n be 60 minutes which will make the last term r^59 because of (n-1).

I usually get confused by this. What is the best way to sort this out ? Will appreciate any help with strategy to know the n part. Here as it appears n should be 61, but why and how.

Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: A strain of bacteria multiplies such that the ratio of its p  [#permalink]

### Show Tags

I have 1 very basic confusion. Since the interval is 60 minutes, shouldn't n be 60 minutes which will make the last term r^59 because of (n-1).

I usually get confused by this. What is the best way to sort this out ? Will appreciate any help with strategy to know the n part. Here as it appears n should be 61, but why and how.

Think about it in terms of beginning of a minute to end of a minute. From beginning of 1st minute to end of 1st minute, from beginning of 2nd minute (which is the same as end of 1st minute) to end of second minute and so on till beginning of 60th minute to end of 60th minute - in 60 minutes the bacteria grew 8 times.
If the ratio of growth every minute is R, at the end of 1st minute, it became R times 5 million. After the end of 2nd minute, it became R^2 times 5 million.
So at the end of 60th minute, it became R^60 times 5 million.

I do understand that GP formula gives
Last term (A60) = First term * R^59
But that is so because R is multiplied for the first time to first term to get the second term. Here, after 2 mins, R has been multiplied to the initial value twice. So it will always depend on context. In time related questions, think in terms of beginning and end of the time period.
_________________
Karishma
Veritas Prep GMAT Instructor Re: A strain of bacteria multiplies such that the ratio of its p   [#permalink] 01 Dec 2019, 23:35
Display posts from previous: Sort by

# A strain of bacteria multiplies such that the ratio of its p  