Percentage increase question

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Sun May 03, 2009 7:43 pm

Hi folks,
This could be tricky problem, if one doesnt pay attention....
Here are two versions. Pls comment on this.

Version 1:
-------------
What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1970

Version 2:
--------------
What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1980

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Source: Beat The GMAT — Data Sufficiency | Sun May 03, 2009 7:43 pm

btg760: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Sun May 03, 2009 7:12 am; Thanked: 6 times

Re: Percentage increase question

by btg760 » Sun May 03, 2009 7:56 pm

vittalgmat wrote:Hi folks,
This could be tricky problem, if one doesnt pay attention....
Here are two versions. Pls comment on this.

Version 1:
-------------
What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1970

Version 2:
--------------
What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1980

The answer of version 1 should be (C) and answer for version 2 should be (B).

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lilu: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Dec 10, 2008 5:13 pm; Location: SF, CA; Thanked: 12 times

by lilu » Sun May 03, 2009 8:20 pm

I think the answer to both versions of the question is B

First version:
Let 1970=100
Then, 1980=100*1.2=120
And 1990=100*1.3=130
And the % increase from '80 to '90 is 120/130~9.2%

Second version:
Let 1970=100
Then, 1980=100*1.2=120
And 1990=120*1.3=156
And the % increase from '80 to '90 is 120/156~7.6%

B in both cases

The more you look, the more you see.

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

Re: Percentage increase question

by Vemuri » Sun May 03, 2009 8:23 pm

vittalgmat wrote: Version 1:
-------------
What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1970

%increase = (pop of(1990)-pop of(1980))/pop of(1980)

Stmt1: Insufficient
Stmt2: pop of 1980 = pop of 1970(1+1/5) ==> (6/5) pop of 1970
pop of 1990 = pop of 1970(1+3/10) ==> (13/10) pop of 1970

From this we can determine the % increase ==> pop of 1970( 13/10 - 6/5)/(6/5) pop of 1970 ==> 1/12 ==> ~8% increase

vittalgmat wrote: Version 2:
--------------
What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1980

%increase = (pop of(1990)-pop of(1980))/pop of(1980)

Stmt1: Insufficient
Stmt2: pop of 1980 = pop of 1970(1+1/5) ==> (6/5) pop of 1970
pop of 1990 = pop of 1980(1+3/10) ==> (13/10) pop of 1980 ==> (13/10)(6/5) pop of 1970

From this we can determine the % increase ==> pop of 1970( (13/10)(6/5) - 6/5)/(6/5) pop of 1970 ==> (3/10) ==> ~8% increase

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vittalgmat: Legendary Member; Posts: 621; Joined: Wed Apr 09, 2008 7:13 pmFollowed by: 4 members; Thanked: 33 times

by vittalgmat » Sun May 03, 2009 9:43 pm

Thanks for the replies.

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missrochelle: Master | Next Rank: 500 Posts; Posts: 117; Joined: Wed Jun 09, 2010 7:02 am

by missrochelle » Wed Sep 01, 2010 9:44 am

lilu wrote:I think the answer to both versions of the question is B

First version:
Let 1970=100
Then, 1980=100*1.2=120
And 1990=100*1.3=130
And the % increase from '80 to '90 is 120/130~9.2%

Second version:
Let 1970=100
Then, 1980=100*1.2=120
And 1990=120*1.3=156
And the % increase from '80 to '90 is 120/156~7.6%

can someone explain how you use #s on this example, when they don't give you numbers to use --- how can u make these assumptions? if we let 1970 = 100 ,is it just because 1970 is the "benchmark" to which they are both being compared?

B in both cases

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