What was the percent increase in the population of City K from 1980 to

Statement 1:
Tells us about population in 1970 and nothing else, so this alone is insufficient.

Statement 2:
Tells us that in 1980 population is 20% more than it was in 1970. Say it was x in 1970, then in 1980 it is 1.2x.
Also given that in 1990 population is 30% more than it was in 1970. Say it was x in 1970, then in 1990 it is 1.3x.

Percent Increase from 1980 to 1990 = (1.3x-1.2x)*100/1.2x (Although you don't need to calcluate it, as answer is not required to be filled in anywhere.

As statement 2 alone can answer the question, so Answer B.

Let the population of 1970 = 100

so population of \(1980 = 120\)

thus population of \(1990 = 130\)

percentage increase \(= \frac{10}{120}*100\)

The answer is B

((90 - 80 )/ 80 )*100

1. Not sufficient

we dont know anything about 80 or 90.

2. Sufficient

70 80 90
x 120x/100 130x/100

from this we can easily find out ((80-90)/80 )*100

Answer is B.

B..
Let population in 1970=100
Then, in 1980= 120
in 1990= 130

We can easily find the percent increase from 1980 to 1990 now..

Statement 1 is clearly unsufficient since there is no information about 1980 nor 1990.
Statement 2 ables to deduce the solution but only if we have the 1970's population. (unsufficient)
Hence, answer C

Target question: What was the percent increase in the population of City K from 1980 to 1990 ?

Statement 1: In 1970 the population of City K was 160,000
Since we're given no information about the population in 1980 or 1990, it's impossible to answer the target question.
Statement 1 is NOT SUFFICIENT

Statement 2: In 1980 the population of City K was 20 percent greater than it was in 1970, and in 1990 the population of City K was 30 percent greater than it was in 1970.
Let x = the population in 1970
So, 1.2x = the population in 1980
And 1.3x = the population in 1990

Percent increase = (100)(1990 population - 1980 population)/(1980 population)
= (100)(1.3x - 1.2x)/(1.2x)
= (100)(0.1x)/(1.2x)
= 10/1.2
So, the percent increase = 10/1.2 percent (we need not actually evaluate the actual fraction)

Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Statement (2) alone gives you sufficient info to the answer the question. Here's an explanation on YouTube

https://www.youtube.com/watch?v=MXotMPU ... PA9GX6g4I4

As an FYI, percent change is a CRUCIAL subject to know for the GMAT!!!

Answer (B)

Classic "C trap." If you mistakenly consider conditions #1 and #2 together, then of course they will work, because condition #2 works by itself.

The trick is having the discipline to never arrive at that step. On DS, if condition #2 is sufficient by itself, and condition #1 is insufficient by itself, then you are done: the answer is Choice B.

Also, if you have a hard time understanding condition #1, then you can use the alternative BD / ACE method instead of the classic AD / BCE method, which allows you to start with condition #2 instead of condition #1.

This "backwards" method makes it clear—if you understand that condition #2 is sufficient—that the answer here must be either Choice B or Choice D.

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