Here is why. follow the stem step-by-step

Four years ago, Adam bought a plot for an amount which was 3 times the amount paid by Ben for another plot.

So 4 years ago we have the following scenario (math translated into words )

Adam=A

which was means =

3 times the amount paid by Ben

translation

A=3B


Today the price of Adam’s plot is twice the price of Ben’s plot.B

Today means after 4 years therefore is A+4 for adam plot

is means =

twice the price of Ben’s plot.

2( Ben plot AFTER 4 years)

2(B+4)

Let me know if now is more clear sir

More on translating words into math

https://gre.myprepclub.com/forum/gre-ma ... 24952.html

Before 4 years:
let ben's plot is x, then adam's plot is 3x

today lets bens plot is y, then adam's plot is 2y

then percent change for adam = (2y - 3x) /3x *100 -> eq 1
then percent change for ben = (y - x) /x * 100 -> eq 2

multiplying 3 in numerator and denominator in eq 2, eq 2 becomes

(3y - 3x) /3x * 100

so subtracting eq 1 from eq2 ,we get

y/3x

which is always positive as y and x are prices. So quantity b is always greater than a. So answer is B

Sir, could you explain more why we can directly +4 to A,B. I totally understand the x2, x3 but Ain't A,B refer to the price of the plots (as we can x2 or x3 to them)? but how can we +4 (years) to A,B (which is price) as well

I ma not quite sure I got what you mean sir.

However, an again

We have A and B

because B is three times than A we have A and 3B

Put the two quantity =

A=3B

(The above according to the stem and translating it into math)

Now, fast forward 4 years we have

A+4 (4 years more)

and 3B+4 (for years more)

Now we have the same equation but after four years

So

A=3B

A+4=2(B+4)

According always to the stem.

Today the price of Adam’s plot is twice the price of Ben’s plot. which is after 4 year

Because A=3B we can substitute in the second equation

3B+4=2(B+4)

3B+4=2B+8

3B-2B=8-4

B=4

A=3B

A=3*4

A=12

Now

A= 12 and B =4 they were 4 years ago

Now after 4 years

A=12+4=16

B=4+4=8

--------------------------- Percent Change-----------------

A was 12 and after 4 years is 16

% change is 4/12=1/3 actually is 33% (be agile with your mind)

B was 4 and now is 8 so is double than that and this a 100% increase

A increased by 33% just

B is the answer

Thank you for you reply. Let me show what I had to clarify

4 years ago
Let Adam's plot's price = A
Let Ben's plot's price = B
Then A = 3B (as Adam bought a plot for an amount which was 3 times than Ben's)

Now (as we don't now if the prices changed or not, so annotate another varieble)
Let Adam's plot's price = X
Let Ben's plot's price = Y
Then X=2Y (as today the price of Adam’s plot is twice the price of Ben’s plot.)

%change Adam = (X-A)/A *100
%change Ben = (Y-B)/B *100

and I stuck here.

also, back to the first question, I cannot warp my head around how can we directly + 4 into A and B as in A=3B become A+4 = 2(B+4)
as they are the price like let's say it xx$ = A and yy$ = B; how can we just have xx$ + 4 years = 2(yy$ + 4 years)

Hope this can clarify my point. Thank you so much in advance for helping out

Yes, I agree with your point. I don't think we can just add 4 years to the price. If they would have been ages, Yes. But not to price.
Also, there is no way to know that price of both the plot increased over time.

FOr eg. If B=100 then A = 300 & Y=200 then X=400
So, Percent change for Adam = (400-300)/300*100 = 33.33%
Percent change for Ben = (200-100)/100*100 = 100%
In this case (B)>(A)

But if Y=50 then X=100
Therefore, Percentage change (-ve) for Adam becomes = (300-100)/300*100= 66.66%
And percentage change (-ve) for Ben = (100-50)/100*100 = 50%
in this case (A)>(B)

Therefore answer should be Option D

This question appeared today in the sunday

GRE Practice Quiz (July 28, 2024) - Quant, Data Analysis, Text Completion, Sentence Equivalence

Hosted by Narenn


Now, aside to set up equation for the previous period of time (four years ago) and now, the question can be solved in a more direct way

The price of plot was , for example, A=90 and B=30

After 4 years

A=100 and B =50

The % change is A=11% and B is 40%

B is the right choice

Or we can solve even with ratios

A:B=3:1

Then

A:B=2:1

Clearly the ratio of B is greater than A because A had a shift of 33% and B is 100%

Again, B is the answer

lets say, Ben plot is 100 dollar at about 4 years ago, then since Adam got him 3times of Ben's price that will be, 300 dollar.
Assuming today Ben's plot appreciated to 400 dollars, double of that would be the price of Adam's plot which is equal to 800 dollar.
%change=(difference/originalx100)
Quantity A
% change in Adam's plot
original=300 dollars
later= 800 dollars
%change=(800-300/300x100)=166.6%

Quantity B
% change in Bens plot
original=100 dollars
later=400 dollars
%change=(400-100/100x100)=300%

B is greater

Initially

A=3b ; B = b

Currently

A = 2x ; B = x

Option B => |(x-b)|/b

Option A => |(2x - 3b)|/3b = 1/3 * 2 [{(2x- 2b)/2b} -0.5} = 2/3 ( Option B - 0.5) = 2/3 Option B - 0.33

Clearly, Option B is larger.