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By what percent did the median household income in Country Y decrease

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GMATD11
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By what percent did the median household income in Country Y decrease [#permalink] New post  14 Feb 2011, 00:25
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A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

73% (01:10) correct 27% (01:16) wrong based on 1372 sessions

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By what percent did the median household income in Country Y decrease from 1970 to 1980 ?

(1) In 1970 the median household income in Country Y was 2/3 of median household income in Country X.
(2) In 1980 the median household income in Country Y was 1/2 of the median household income in Country X.

Show Spoiler
Let median household income in Country Y is y
Let median household income in Country X is x

a) in 1970 y=2/3x
not sufficient
b) in 1980 y=1/2x
not sufficient

Combining a and b

%decrease = (1/2x-2/3x) /2/3x

C

But it is wrong
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AmrithS
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Re: By what percent did the median household income in Country Y decrease [#permalink] New post  14 Feb 2011, 00:53
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Let the median income of country Y be y for 1970
Let the median income of country X be x for 1970

Let the median income of country Y be y' for 1980
Let the median income of country X be x' for 1980

Question: (y'-y)/y * 100 = ?

Statement 1:
In 1970, y = (2/3)x
It tells us nothing about y'
So, not sufficient

Statement 2:
y' = (1/2)x'
It tells us nothing about the relation with y

Both Statements Together:
y = (2/3)x
y' = (1/2)x'

Now, we have no way of equating the two data.
So Not sufficent

Ans: 'E'
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AmrithS
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Re: By what percent did the median household income in Country Y decrease [#permalink] New post  14 Feb 2011, 00:56
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GMATD11 wrote:
Let median household income in Country Y is y
Let median household income in Country X is x

a) in 1970 y=2/3x
not sufficient
b) in 1980 y=1/2x
not sufficient

Combining a and b

%decrease = (1/2x-2/3x) /2/3x

C

But it is wrong


You can't assume that the median has remained unchanged from 70s to 80s
So you must assign different variables for the median in year 70 and 80 for both town X and Y!
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fluke
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Re: By what percent did the median household income in Country Y decrease [#permalink] New post  14 Feb 2011, 01:09
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GMATD11 wrote:
91)By what % did the median household income in country Y decrease from 1970 to 1980?
a) In 1970 the median household income in Country Y was 2/3 of the median household income in Country X
b) In 1980 the median household income in Country Y was 1/2 of the median household income in Country X

Let median household income in Country Y is y
Let median household income in Country X is x

a) in 1970 y=2/3x
not sufficient
b) in 1980 \(\color{red}{y=1/2x}\)
not sufficient
"x" may not be median household income for country x in 1980. It could be (x+100) or (x-89) or (x*4.5)


Let's take some numbers;
1970:
Median income for x: 90
Median income for y = (2/3)*90 = 60

1980
Median income for x: 120
Median income for y = (1/2)*120 = 60

Percent decrease: 0%

case II:
1970:
Median income for x: 90
Median income for y = (2/3)*90 = 60

1980
Median income for x: 30
Median income for y = (1/2)*30 = 15

% decrease for y = 45/60*100 = 75%

Ans :"E"
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Re: By what percent did the median household income in Country Y decrease [#permalink] New post  14 Feb 2011, 01:13
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The answer would have been C is some additional info was given in the main statement. Info like,

if the median for city x remained unchanged from 1970 to 1980, what is the percentage change in the value of the median for city y from 1970 to 1980.
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Re: By what percent did the median household income in Country Y decrease [#permalink] New post  14 Feb 2011, 06:45
both the options do not provide any clues of changing house hold income from 1970 to 1980.
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Re: By what percent did the median household income in Country Y decrease [#permalink] New post  27 Aug 2014, 04:28
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GMATD11 wrote:
By what % did the median household income in country Y decrease from 1970 to 1980?

(1) In 1970 the median household income in Country Y was 2/3 of the median household income in Country X
(2) In 1980 the median household income in Country Y was 1/2 of the median household income in Country X

Show Spoiler
Let median household income in Country Y is y
Let median household income in Country X is x

a) in 1970 y=2/3x
not sufficient
b) in 1980 y=1/2x
not sufficient

Combining a and b

%decrease = (1/2x-2/3x) /2/3x

C

But it is wrong


Similar question to practice: from-january-1-2002-to-july-1-2002-the-median-household-173769.html
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kokus
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Re: By what percent did the median household income in Country Y decrease [#permalink] New post  18 Jun 2020, 14:27
So, if we had the info that the median of household in country X did not change from 1970 to 1980, can solve by making x equal in two y:x ratios e.g.

1970: y/x = 2/3 (multiply by 2)
1980 = y/x = 1/2 (multiply by 3)

1970: y/x = 4/6
1980: y/x = 3/6

x household income: 1970: 1980: 4:3 (25% decrease)?
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Re: By what percent did the median household income in Country Y decrease [#permalink] New post  06 Oct 2022, 03:10
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Re: By what percent did the median household income in Country Y decrease [#permalink]
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