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GMATD11
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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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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both the options do not provide any clues of changing house hold income from 1970 to 1980.
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GMATD11
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

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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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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