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

Question

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.

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

AmrithS · Accepted Answer

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'

AmrithS · Answer

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!

fluke · Answer

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"

AmrithS · Answer

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.

MHIKER · Answer

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

Bunuel · Answer

Similar question to practice: from-january-1-2002-to-july-1-2002-the-median-household-173769.html

kokus · Answer

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)?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards