NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 16:42 It is currently 25 Apr 2024, 16:42
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Four hours from now, the population of a colony of bacteria will reach

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
carcass
Board of Directors
Joined: 01 Sep 2010
Posts: 4384
Own Kudos [?]: 32878 [100]
Given Kudos: 4455
Send PM
Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   02 Jul 2017, 12:00
6
Kudos
94
Bookmarks
Top Contributor
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

70% (01:49) correct 30% (01:55) wrong based on 2968 sessions
Hide Show timer Statistics
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29930 [29]
Given Kudos: 799
Location: Canada
Send PM
Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   Updated on: 20 Jan 2020, 08:21
17
Kudos
11
Bookmarks
Expert Reply
Top Contributor
carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

6.4 * \(10 ^ 2\)
8.0 * \(10 ^ 4\)
1.6 * \(10 ^ 5\)
3.2 * \(10 ^ 5\)
8.0 * \(10 ^ 6\)


Let's work backwards.

Population 4 hours in future: 1.28 x 10^6
Population now: 0.64 x 10^6 (half the population 4 hours in future)
Population 4 hours ago: 0.32 x 10^6 (half the current population)
Population 8 hours ago: 0.16 x 10^6 (half the population 4 hours ago)
Population 12 hours ago: 0.08 x 10^6 (half the population 8 hours ago)

Now check the answer choices.
Only answer choices B and E have the same format with 8 times some power of 10
Answer choice E definitely doesn't match, so the correct answer must be B

For any doubters out there, notice that:
0.08 x 10^6 = (8.0) x (10^-2) x 10^6
= 8.0 x 10^4

Answer:
Show Spoiler
B

Originally posted by BrentGMATPrepNow on 02 Jul 2017, 14:48.
Last edited by BrentGMATPrepNow on 20 Jan 2020, 08:21, edited 1 time in total.
General Discussion
avatar
B
Manbarasan
Intern
Intern
Joined: 26 Mar 2017
Posts: 13
Own Kudos [?]: 9 [4]
Given Kudos: 12
Location: India
Schools: Great Lakes '19
GMAT 1: 580 Q47 V23
GPA: 3.1
Send PM
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   02 Jul 2017, 12:16
3
Bookmarks
Population after 4 hours is given, take it as x

So current population is x/2

Before 12 hours is x/16

Option B




Sent from my iPhone using GMAT Club Forum
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5205 [0]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   02 Jul 2017, 12:18
These kind of questions, are best done when we go backwards.

1280000 when halved gives 640000(4 hours ago)
4 more hours ago the population of the colony of bacterial colony would be 320000
4 more hours ago, the population will be 160000
4 more hours ago, the population will be 80000 which is 8 * \(10 ^ 4\)(Option B)
avatar
B
GC2808
Intern
Intern
Joined: 31 Jul 2017
Posts: 7
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   16 Oct 2017, 18:23
It is possible to do using powers to simplify:
(future) 1.28 x 10^6
Going back 4 times from +4y to -12y: multiply by 1/(2^4)
1.28 x 10^6 = 128 x 10^4 = 2^7 x 10^4 == you could stop here looking to the possible answers
(2^7 x 10^4) / 2^4 = 2^3 x 10^4 = 8 x 10^4
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22052 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   19 Oct 2017, 10:26
1
Bookmarks
Expert Reply
carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)



Since the population doubles every 4 hours and the population will be 1.28 x 10^6 four hours from now, the current population must be half of 1.28 x 10^6, or ½(1.28 x 10^6) = 0.64 x 10^6.

Thus:

4 hours ago, the population was half the current population: ½(0.64 x 10^6) = 0.32 x 10^6.

8 hours ago, the population was half the population 4 hours ago: ½(0.32 x 10^6) = 0.16 x 10^6.

Finally, 12 hours ago the population was half the population 8 hours ago: ½(0.16 x 10^6) = 0.08 x 10^6 = 8 x 10^-2 x 10^6 = 8 x 10^4.

Answer: B
User avatar
B
lichting
Intern
Intern
Joined: 17 Sep 2017
Posts: 37
Own Kudos [?]: 37 [0]
Given Kudos: 169
Send PM
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   15 Jan 2018, 03:33
It will double every 4 hour => if 4 hours from now the population is 1.28 * 10^6
=> now the population is 1.28 * 10^6 / 2

It will double (x2) every 4 hour => 12 hours ago, the population is 1/ 2^ 3 = 1/8 the population now (3 = 12/4)
=> The population 12 hours ago = 1.28 * 10^6 /2 * 1/8 = 8 * 10^4

=> B
User avatar
L
dave13
VP
VP
Joined: 09 Mar 2016
Posts: 1160
Own Kudos [?]: 1017 [0]
Given Kudos: 3851
Send PM
Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   06 May 2018, 06:19
carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)



pushpitkc, is my approach / reasoning correct ? :)

1.28 * \(10 ^ 6\) means we need to move decimal point 6 points to the right so it is 1,280,000, so i just leave out zeros and work with 128

if in 4 hours the population will be 128, then now it is 64

4 hours ago it was 32
8 hours ago 16
12 hrs ago 8

so all i need is to add 4 zeros and express it like this \(8*10^4\) :)

one thing I didn't get why in answer option B. 8.0 * \(10 ^ 4\) \(8\) is expressed as \(8.0\) and not just \(8\) I mean with one zero after decimal point... :?
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5205 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   06 May 2018, 08:13
1
Kudos
dave13 wrote:
carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)



pushpitkc, is my approach / reasoning correct ? :)

1.28 * \(10 ^ 6\) means we need to move decimal point 6 points to the right so it is 1,280,000, so i just leave out zeros and work with 128

if in 4 hours the population will be 128, then now it is 64

4 hours ago it was 32
8 hours ago 16
12 hrs ago 8

so all i need is to add 4 zeros and express it like this \(8*10^4\) :)

one thing I didn't get why in answer option B. 8.0 * \(10 ^ 4\) \(8\) is expressed as \(8.0\) and not just \(8\) I mean with one zero after decimal point... :?


Hi dave13

This problem is best solved when we go backwards!

8 *10^4 = 80000
Now see the sequence when we double the population of the colony of bacteria
80000 * 2 = 160000 | 160000 * 2 = 320000 | 320000 * 2 = 640000 | 640000 * 2 = 1280000
(You can see that 12 hours from the start, the population has increased
from 8 *10^4 to 6.4 *10^5 and then to 1.28 * 10^6)

Your approach is perfect otherwise. All you need to understand is this part of why the ZEROES increase!

Hope this helps you!
avatar
S
ColumbiaEMBA
Manager
Manager
Joined: 29 Sep 2017
Posts: 89
Own Kudos [?]: 60 [0]
Given Kudos: 10
Location: United States
Send PM
GMAT ToolKit User Reviews Badge
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   06 May 2018, 14:13
1.28E6 = 128E4. 12 hours before now = 2^4 --> 128E4 / 2^4 = 128E4 / 16 = 128/16 = 8E4.
User avatar
S
suganyam
Intern
Intern
Joined: 19 Jan 2019
Posts: 40
Own Kudos [?]: 9 [1]
Given Kudos: 65
Send PM
Reviews Badge
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   06 Feb 2020, 14:53
1
Kudos
backwards (1.28*10^6)/2 ---present time
(1.28*10^6)/4 ---4 hrs before
(1.28*10^6)/8--- 8 hrs before
(1.28*10^6)/16 --- 12 hrs before
ans 8*10^4
User avatar
G
CEdward
VP
VP
Joined: 11 Aug 2020
Posts: 1262
Own Kudos [?]: 201 [0]
Given Kudos: 332
Send PM
Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   11 Apr 2021, 22:27
Upsetting this took me over 5 minutes just to try and understand the doubling, etc.

4 hours from now the population doubles to 1.28 * 10^6

This means the CURRENT population is half of this. Then we have to go back 3 doublings so 2^4

1.28 * 10^6 / 2^4 = 128 x 10^4 / 2^4 = 2^7 x 10^5 / 2^4 = 8 x 10^4

B
User avatar
B
Rail
Intern
Intern
Joined: 29 Sep 2021
Posts: 22
Own Kudos [?]: 5 [0]
Given Kudos: 7
Send PM
Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   02 Jul 2022, 00:27
As GC2808 says, first you need to speed up this problem by switching from 1,28*10^6 to 128*10^4.

Then you need to observe that are 4 periods in which the population doubles (16 hours total, 4 hours each interval) that need to take into account for "discounting" the final value of the population.

So you basically do (128*10^4)/2^4

(128*10^4)/16 results in 8*10^4.

There are no casual numbers here (and probably in none of the GMAT problems)

The key here is the first step. Doing that leads you to solve the problem in 2 min or less
User avatar
G
ThatDudeKnows
Tutor
Joined: 11 May 2022
Posts: 1092
Own Kudos [?]: 697 [1]
Given Kudos: 81
Send PM
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   02 Jul 2022, 06:21
1
Kudos
Expert Reply
carcass wrote:
Four hours from now, the population of a colony of bacteria will reach 1.28 * \(10 ^ 6\). If the population of the colony doubles every 4 hours, what was the population 12 hours ago?

A. 6.4 * \(10 ^ 2\)
B. 8.0 * \(10 ^ 4\)
C. 1.6 * \(10 ^ 5\)
D. 3.2 * \(10 ^ 5\)
E. 8.0 * \(10 ^ 6\)


Why on earth would we deal with scientific notation?

4 hours from now: 1280000
Now: 64000
4 hours ago: 32000
8 hours ago: 16000
12 hours ago: 8000

Answer choice B.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32679
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink] New post   08 Jul 2023, 11:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Four hours from now, the population of a colony of bacteria will reach [#permalink]
08 Jul 2023, 11:03
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions