We'll translate the stmts into equations to better understand what we need to do.
This is a Precise approach.

(1) Written as an equation, this is
2002 population = 2001 population *1.02 and 2001 population * 0.02 = 20,000.
This is two equations with two variables -- sufficient.

(2) Written as an equation, this is:
2001 population = 1,000,000.
We have no information on 2002 population -- insufficient.

(A) is our answer
_________________

Solution

Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are asked to find the population of city X in 2002.

We do not have much information to infer from, let us move to analyse the statements.

Step 3: Analyse Statement 1
“X's population in 2002 increased by 2 percent, or 20,000 people, over 2001.”

• Percentage increase in population of city X in 2002 over 2001 = 2%
• Increase in population of city X in 2002 over 2001 = 20,000

o Hence, 2% of population of city X in 2001 = 20,000

 Therefore, we can find the population of city X in 2001 and then 2% increase or 20,000 increase will give the population of city X in 2002.

Thus, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2
“In 2001, X's population was 1,000,000.”
From this statement, we cannot find the population of city X in 2002.

Thus, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)
Since we could determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer is option A.


_________________

DavidTutorexamPAL nick1816 VeritasKarishma MentorTutoring


Could you advise what is incorrect in below approach:

St 1:
X's population in 2002 increased by 2 percent over 2001. -> P(2001) * 1.02 = P(2002)
i.e.
X's population in 2002 increased by 20,000 people over 2001. -> P (2002) = P (2001) + 20,000

Suff.

Unfortunately, hurriedly I too selected C with this thought:
To find a final value, I need initial value and change of %tage or difference hence I need to use St 2.
I could not form two linear eqs of (1) under timed conditions.
_________________

Hello, adkikani. Keep in mind that with DS questions in particular, you often do not need to actually solve the problem to answer the question. Here, we are asked about an exact value of a population at a specific point in time: we need to be able to to determine the population of City X in 2002, nothing more. A quick scan of the two statements reveals that they both provide information on 2001, so STOP. Ask yourself, what would we need to know about 2001 to determine the population for 2002? Either a rate of growth with some sort of total attached or a difference in the total number of people, as long as you had a baseline population, would do. Now you can assess the statements. I like to start with the easier looking of the two, so I would pick (2) first.

Clearly, Statement (2) does not deliver on our pre-thinking for the problem. We get a population from the year before, but nothing more. With no basis for comparison, we cannot predict what happened the next year. Mark off (B) and (D) as answer choices. How about Statement (1)?

Aha. If 2 percent corresponds to 20,000 people, and you understand that there was a growth or increase in population, then you could calculate the population in either 2001 or 2002. Note that without the word increased, the change would be unknown, whether the population had gone up or down, and the answer would be insufficient. As is, however, you could work out pretty quickly that 1 percent of 1,000,000 is 10,000 just by moving the decimal two places to the left, so two 1 percents would be 2 * 10,000, or 20,000 people. Thus, the original population was 1,000,000, and we know that Statement (1) is SUFFICIENT. The answer is (A).

I did not do anything more than solve this one through reasoning. Whenever you encounter DS problems, always ask yourself three things:

1) What is the question asking?
2) What do I know? (i.e. What information is provided?)
3) What would I need to know to answer the question that is being asked?

Such an approach can spare you all the work sometimes, and you will be less prone to falling into traps. I hope this may help you in your studies.

- Andrew

You don't have to form linear equations. This is what I thought when I read statement 1.

(1) X's population in 2002 increased by 2 percent, or 20,000 people, over 2001.

So, 2% of 2001 population is 20,000. This means I can get 2001 population. This means I can add 20,000 to it and get 2002 population.
Sufficient.

(2) In 2001, X's population was 1,000,000.

Ok, I have 2001 population. But what about 2002 population? By how much did it increase/decrease compared with 2001 population? Not given.
Not sufficient.
_________________

(1) Let, the population of city \(X\) in 2001 was \(P\)

\(P*\frac{2}{100}=2000\)

\(P=200,000 \)

Population in 2002\(=200,000+20,000=220,000\) Sufficient.

(2) Doesn't give any information to go to the population of 2002. Insufficient.


The answer is \(A\)
_________________