Two months from now, the population of a colony of insects

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Two months from now, the population of a colony of insects

by BTGmoderatorDC » Tue Jul 23, 2019 5:35 pm

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Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4

OA B

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Tue Jul 23, 2019 5:35 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Tue Jul 23, 2019 10:20 pm

BTGmoderatorDC wrote:Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4

OA B

Source: Veritas Prep

Given: Population in 2 months from now = 3.2 * 10^4;

Question: What's the population 8 months ago?

So, we have to find out the population 10 months ago from the point when the population would be 3.2 * 10^4.

Since the population doubles every 2 months, it will have 10/2 = 5 periods of compounding. Thus, the population would have been 1/2^5 = 1/32 times 8 months ago.

Thus, population 8 months ago = (3.2 * 10^4) / 32 = (32 * 10^3) / 32 = 10^3

The correct answer: B

Hope this helps!

-Jay
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Jul 24, 2019 4:46 am

BTGmoderatorDC wrote:Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4

OA B

Source: Veritas Prep

Let's use a growth table to work backwards

If the population DOUBLES every 2 months we travel into the future, we can also say that the population is HALVED every 2 months we travel into the past

2 months from now: population = (3.2)(10^4)
Now: population = (1/2)(3.2)(10^4) = (1.6)(10^4)
2 months ago: population = (1/2)(1.6)(10^4) = (0.8)(10^4)
4 months ago: population = (1/2)(0.8)(10^4) = (0.4)(10^4)
6 months ago: population = (1/2)(0.4)(10^4) = (0.2)(10^4)
8 months ago: population = (1/2)(0.2)(10^4) = (0.1)(10^4)

(0.1)(10^4) isn't among the answer choices, so let's REWRITE it.

(0.1)(10^4) = (1)(10^-1)(10^4)
= (1)(10^3)

Answer: B

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jul 31, 2019 4:25 pm

BTGmoderatorDC wrote:Two months from now, the population of a colony of insects in a remote area will reach 3.2 * 10^4. If the population of the colony doubles every two months, what was the population eight months ago?

a) 3.6 * 10^2
b) 1.0 * 10^3
c) 2.0 * 10^3
d) 1.6 * 10^4
e) 2.6 * 10^4

OA B

Source: Veritas Prep

The population currently must be 3.2 * 10^4 / 2 = 1.6 * 10^4. So, 2 months ago, the population was 1.6 * 10^4 / 2 = 0.8 * 10^4; 4 months ago, the population was 0.8 * 10^4 / 2 = 0.4 * 10^4; 6 months ago, the population was 0.4 * 10^4 / 2 = 0.2 * 10^4; and, 8 months ago, the population was 0.2 * 10^4 / 2 = 0.1 * 10^4 = 1.0 * 10^3.

Answer: B

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