In Country C, the unemployment rate among construction worke

September 1, 1992
The total number of construction workers = 1,000 (assume);
16% are unemployed, thus the number of unemployed workers = 160.

September 1, 1996
The total number of construction workers = 1,200 (20% greater);
9% are unemployed, thus the number of unemployed workers = 108.

Decrease is 52, which is approximately 30% of 160.

Answer: B.
_________________

Yes, you can do it using the successive percentage change concept too.

Number of unemployed construction workers = Number of Construction Workers * Unemployment rate

If there is a change in the number of construction workers and unemployment rate, we can find the change in the number of unemployed construction workers.

Number of construction workers is 20% greater i.e. 6/5 of previous value
Unemployment rate reduces from 16 to 9 i.e. becomes 9/16 of previous value

Multiplier for number of unemployed construction workers = 6/5 * 9/16 = 27/40

This is a reduction of 13/40 which is a little more than 30%.
_________________

From 92 - 96 -> 20% inc in # construction workers
From 92 - 96 -> 7% dec in unemployment -> +7% to # of construction workers
20% + 7% = 27% -> (B -> 30%)

Since the problem is percentage related, I just assumed the total number of workers in 1992 was 100.
=> total unemployed in 92 = 16
There was a 20% increase in the number of workers between 92 and 96
=> Total workers in 96 = 100 + 100(20/100) = 120.
There was a change of 9% in the unemployment rate from 92 to 96.
=> Total unemployed in 96 = 120 * 9/100 = 11 (approximately)

Now the actual question - change in the unemployed construction workers
=> (unemployed in 92 - unemployed in 96) / unemployed in 92
=> (16-11)/16 * 100
= -30 approximately.
=> 30% decrease.

This problem is a prime candidate for picking numbers. Since the question is dealing with percents I decided to go use 100. Once you pick easy to work with numbers just pick apart the questions slowly

Unemployment rate 1992 was 16%
---> I'm starting with 100 workers therefore 16 are unemployed

In 1996 the number of workers increased 20% ---> there are now 120 workers.
---> 9% unemployed would equal to 10.8% (the question uses the word approximately which told me I'm definitely rounding some numbers) so 11%

Percent change formula [Difference][/Original] X 100 = [5][/16] X 100 = ~30%

Assume there are 1000 construction workers in the year 1992.
Then tabulate as per the question

1996 1992
Contruction Workers 1200 1000
Unemployed Workers 108 160


Simply find out...((final - initial)/initial)*100

Option B is right

In CountryC, the unemployment rate among
construction workers dropped from 16 percent on
September 1,1992, to 9 percent on September 1,
1996. If the number of construction workers was
20 percent greater on September 1,1996, than on
September 1,1992, what was the approximate
percent change in the number of unemployed
construction workers over this period?
(A) 50% decrease
(B) 30% decrease
(C) 15% decrease
(D) 30% increase
(E) 55% increase

In OG explanation is given but its too much time consuming and confusing for me. Anyone has tried any other way ??? Or anyone has tried to solve this question with pick number strategy...I tried but I am not getting correct answer.

Please explain

Thanks in advance.

1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11

% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B

Anyone did this without picking numbers?

say in 1992 - 25 ppl & 16% unemployment rate then 4 ppl .
say in 1996 - 20% increase then 30 ppl & 9%unemployment rate then 2.7

4-2.7/4 = 32.5 % then i have chosen B.. pretty time consuming for choosing numbers.

solved it the way bunuel explained.
92 - 1000 workers, 160 unemployed.
96 - 1200 workers, 108 unemployed.
we can see the number decreased. we can eliminate the answer choices that say "increase". moreover, if you think logically, 52 is not 50% of 160, thus we can eliminate it. Moreover, 16=10% and 8 = 5%. decrease of 15% should be 24 workers, which again not works. thus, the only option that is possible - 30%

Solution:

We are given two pieces of information that can be translated into equations. However, before we make those equations let’s set up some variables as well to display some of the information provided.

16% = unemployment rate on September 1, 1992

9% = unemployment rate on September 1, 1996

c = number of construction workers on September 1, 1992

d = number of construction workers on September 1, 1996

Thus, we know:

0.16 × c = number of unemployed construction workers on September 1, 1992

0.09 × d = number of unemployed construction workers on September 1, 1996

We are asked to determine the approximate percent change in the number of unemployed construction workers over this period.

The formula for percent change is:

[(New Value – Old Value)/(Old Value)] x 100

Using our variables above, the percent change formula will be:

(0.09d – 0.16c)/(0.16c) × 100

In order to solve this formula we need to create an equation. We are given that the number of construction workers was 20% greater on September 1, 1996 than on September 1, 1992. Thus, we can say:

d = c + 0.2c = 1.2c

We can now substitute 1.2c for d in our percent change equation:

[(0.09 × 1.2c – 0.16c)/(0.16c)] × 100

[(0.108c – 0.16c)/(0.16c)] × 100

[(108c – 160c)/(160c)] × 100

[(-52c)/(160c)] × 100

(-13/40) × 100

Since we are asked to approximate we can change -13/40 to -13/39, which reduces to -1/3. We now have:

-1/3 × 100 = -33.3%

The closest answer to this is B, a 30% decrease.

Because the answer choices are in percentage form, there is another way to solve this question: we can use convenient numbers. Let’s say the number of construction workers in 1992 is 100. We know, therefore, that the number of workers in 1996 is 1.2 × 100 = 120 workers.

We know that the unemployment rate among construction workers dropped from 16% on September 1, 1992 to 9% on September 1, 1996.

Thus we can say that the number of unemployed construction workers in 1992 is:

0.16 × 100 = 16

And the number of unemployed construction workers in 1996 is:

120 × 0.09 = 10.8 which is about 11.

We can now get the percent change:

[(New Value – Old Value)/(Old Value)] × 100

Using our values above the percent change formula will be:

[(11 – 16)/16] × 100

(–5/16) × 100

-5/16 is about -5/15, which reduces to -1/3. Again, -1/3 × 100 = -33.3%, which is closest to answer B.
_________________

.09*1.2/.16=.675
1-.675=.325~30% decrease
answer b

Is the above reasoning correct?

This approach latches on the word 'approximate' in the question. First of all, there were more people working in 1996 (20% more than 1992). The % of unemployment in 1996 is lower than 1992 (only 9% compared 16% of 1992). So you have more people working and out of that smaller % unemployed. Meaning, definitely overall fewer people were unemployed in 1996 i.e. DECREASE.

Then, roughly speaking, 20% increase in workers + 7% change in unemployment is 27%. You have two choices closest to 27%. 30% increase or 30% decrease. We already know it is an overall decrease for sure. So it must be APPROXIMATELY 30% overall decrease.

A very neat and quick solution but more error prone if you can't quickly wrap your head around a bunch of numbers being thrown at you. I'd better stick with a number picking solution unless I am on a time crunch mode and I must guestimate a couple of questions.

Description 1992 1996
% of unemployed 16% 9%
number 1 1,2

0,09*1,2-0,16=-0,052
-0,052/0,16=-0,3..

Answer is B 30% Descriase

Bunuel, niks18





I complicated calculations by taking smart no as 100 instead of 1000 since
we normally do so in %tages. What strategy did you use to pick 1000 and not 100?
_________________

Hi adkikani

for % problems, assumption of total to be 100 is the natural inclination for most of us and calculation should not be too complicated. So if you assume 100 then instead of 160 & 108 you will get 16 and 10.8 respectively. these numbers are still small and calculations should not be tough.

However if you are able to think (under 2 minutes in exam pressure) that the % involved are not multiples of 10 so working with them might lead to decimal numbers, then obviously working with 1000 (or higher multiples of 10) will be beneficial as it will result in whole numbers.

it depends on how quickly you are able to recognize the trend.

Hi All,

This question can be solved by TESTing VALUES. You'll need to reorganize the information that you're given though (since it's offered 'out of order').

We're told that the NUMBER of construction workers was 20% greater in 1996 than in 1992.

Number of workers in '92 = 100
Number of workers in '96 = 120

We're told that the UNEMPLOYMENT RATE was 16% in 1992 and 9% in 1996. This allows us to figure out the NUMBER of unemployed workers...

Unemployed in '92 = 100(16%) = 16
Unemployed in '96 = 120(9%) = 10.8

The question asks for the APPROXIMATE Percent Change in the number of unemployed workers...

Percent Change = (New - Old)/Old = Difference/Original

With these numbers, we end up with...

(10.8 - 16)/16 = -5.2/16 = about -1/3 = about a 30% decrease

Final Answer:

GMAT assassins aren't born, they're made,
Rich