During a three-year period, the profits of company X changed by what

During a three-year period, the profits of company X changed by what percent from the second year to the third year?

(1) The increase in profits of company X from the first year to the second year was the same as the increase form the first year to the third year.

Since the increase in profits from 1st year to the 2nd year was the same as the increase from the 1st year to the 3rd year then there was not any increase in profits from the 2nd year to the 3rd year, which means 0% increase from the 2nd year to the 3rd year. Thus, this statement implies that there was no increase from the second year to the third year. Sufficient.

(2) For company X, the profits for the first year were $13,800 and the profits for the third year were $15,900.

We need the profits for the second year. Not sufficient.

Answer: A.­
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let's start with statement (2): It's clearly not sufficient, as we don't have any information about the 2nd year.
(1) This one is tricky. Either you solve this one conceptually (see the solution provided by Bunuel) or using algebra:

Profits
1st year=x
2md year = y
3rd year = z

Percent change
1st - 2nd year:\(\frac{y-x}{x}\)
1st - 3rd year:\(\frac{z-x}{x}\)
And both changes are equal:\(\frac{y-x}{x}=\frac{z-x}{x}\), just do the required manipualtions and you'll get y=z, hence 0% change Sufficient

Hi,

We are looking for increase in profit from 2nd to 3rd year..

Let's see the statements...

(1) The increase in profits of company X from the first year to the second year was the same as the increase from the first year to the third year.
This means there has been no increase in profit from 2nd to 3rd year..
Say if 1st yr it was 2000, 2nd yr it went upto 2200 and third year too it remained 2200...
Hence sufficient

(2) For company X, the profits for the first year were $13,800 and the profits for the third year were $15,900.[/quote]
Nothing about 2nd year.
Insufficient

A
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Got this right. but it looks more like a CR thing than quant. can we really expect this type of question on the test?

Hello

Yes its possible. As per the website, GMAT quant section tests "...your ability to analyse data and draw conclusions using reasoning skills".

Also, "The GMAT exam measures the test taker's ability to assess higher-order reasoning skills (verbal, quantitative, analytical writing and integrated reasoning)..."

There is a possibility that a question might just need reasoning/logic and no calculation at all.

We are looking for the % change from 2nd year to 3rd year.

Let's assign some variables:

F = first year;
S = second year;
T = third year;

% change from S -> T is the same as (T - S)/S

Statement 1:
% change from F->S is the same as F->T

F->S = (S-F)/F
F->T = (T-F)/F

Setting these two equal to each other: we get S = T, thus percent change is 0

Statement 2: We are not given the profits of S, thus it is INSUFF

Answer: A

So I find going through these project butler questions really helps with doing two things:
1. Getting the brain warmed up.
2. Getting quantity and spamming volume.

The trick to getting this question is actually taking a pause on St1 before easily dismissing it.

St1 - Profits between year 1 and 2 is the same as between year 1 and 3.

This implies that the profit didn't actually change at all between year 2 and 3.
e.g. P = 100 in Y1 then a 15% increase means P = 115 in Y2. Similarly, a 15% increase from Y1 to Y3 necessitates that P = 115 in Y3 as well.

In other words, the profit change b/w Y2 and Y3 = 0.

Do this for any other combination of numbers.

St2 - Profits for Y1 = 13800 and Y3 = 15900
Clearly insufficient. You could pick any number for the profit for Y2 out of a hat and it would yield a different answer
e.g. P = -1500000000 (Bankrupt)
P = 15000
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During a three-year period, the profits of company X changed by what percent from the second year to the third year?

Here we are asked to find percentage increase of company's profit from the second year to the third year.

(1) The increase in profits of company X from the first year to the second year was the same as the increase from the first year to the third year.

Since the percentage increase from 1st year to 2 nd year is same as the increase from 1st year to 3 rd year, we can conclude that profit of the company in 2nd year and 3 rd year are the same and ​the percentage increase from 2 nd year to 3 rd year will be 0 %.

Lets explain it through an example.
profit of company X in 1st year = 100 $
Percentage increase of profit from 1st year to 2 nd year = 10 %
profit of company X in 2 nd year = 100 + 10 $ = 110$
percentage increase from 1st year to 3 rd year is 10 % which is same as that of from 1st year to 2 nd year
profit of company X in 3 rd year = 100 + 10 $ = 110$

profit of company X in 2 nd year = profit of company X in 3 rd year = 110$

Since profit in 2nd and 3rd year are not changing, the percentage increase would be 0 %

Statement 1 is sufficient.

(2) For company X, the profits for the first year were $13,800 and the profits for the third year were $15,900

Profit of the company in 2nd year is not mentioned in statement 2, hence it is not sufficient

Option A is the right answer

Thanks,
Clifin J Francis,
GMAT SME
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