In Country C, the unemployment rate among construction worke

Question

In Country C, 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

(A) 50% decrease
(B) 30% decrease
(C) 15% decrease
(D) 30% increase
(E) 55% increase

Bunuel · Accepted Answer

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.

KarishmaB · Answer

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%.

monkeya41 · Answer

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%)

coolparthi · Answer

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.

PanHandle · Answer

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    X 100 =    X 100 = ~30%

ronr34 · Answer

Anyone did this without picking numbers?

ScottTargetTestPrep · Answer

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:

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:

× 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:

× 100

Using our values above the percent change formula will be:

× 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.

gracie · Answer

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

EMPOWERgmatRichC · Answer

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:  B

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

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=9zQfeJsxKMA

GMATinsight · Answer

Answer: Option B

Step-by-Step Video solution by  GMATinsight

https://www.youtube.com/watch?v=tmwU4bil3_U

Elite097 · Answer

KarishmaB  cannot understand your approach how did it become 9/16?
You have skipped multiple steps- can you please elaborate on those? Have seen the links and they do not seem to be using this approach  avigutman

KarishmaB · Answer

Think about what the multiplier is: Ratio of New:Old An increase of 20% -> Multiplier is 6/5 (new value will be 6/5th of old value) A decrease of 25% -> Multiplier is 3/4 (New value will be 3/4th of old value) When we multiply the multiplier by the old value, we get the new value. Since old unemployment rate is 16% and new is 9%, the multiplier will be 9/16. The new unemployment rate is 9/16th of the old one. Check this video: https://youtu.be/HxnsYI1Rws8

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