Boomtown urban planners expect the city’s population to

Question

Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year?

A. 20%
B. 40%
C. 50%
D. 65%
E. 75%

This how I am trying to solve, but I am stuck after this.

If we assume that today’s population is 100, next year it would be 1.1 × 100 = 110, and the following year it would be 1.1 × 110 = 121. If this is double the population of one year ago, the population at that time must have been 0.5 × 121 = 60.5. Because the problem seeks the “closest” answer choice, we can round 60.5 to 60.

Will it be 121-60/60? But this doesn't give me the right answer. Please help.

Bunuel · Accepted Answer

Population now - 100;
Population one year from now - 110;
Population two years from now - 121;

Since the population two years from now (121) is exactly double the population one year ago then the population one year ago was 121/2=60.5.

Now, the question asks about the population increase  over the last year , so from 60.5 (last year) to 100 (now): percent increase=difference/original*100=(100-60.5)/60.5*100=39.5/60.5*100=~2/3*100=~65%.

Answer: D.

Hope it's clear.

ricsingh · Answer

You have the calculation correct till 60.5 but we need the percentage increase of 60.5 to 100.00
=> (100 - 60.5)/60.5 = 65%. even if you round 60.5 to 60 you will reach the correct answer.

PareshGmat · Answer

Look at the table below:

Percentage increase

= 40 * \frac{100}{60}

= 66.66

Answer = D

iliavko · Answer

Am I correct to say that if we write  P*(\frac{11}{10})^2=2S  where P=present population, S= start population, so 1 year ago. 
That gives  S=\frac{121P}{200}  but after this, how can we relate the S to P to solve the question? Does this make sense?..

Like writing  S*\frac{x}{100}=P  gives 160% what's wrong here?..

Thank you!

ajdse22 · Answer

While solving the question, I used hit and trial using some number sense.
So I know since the number doubled after two years when compared to what was year ago.
let us say year ago was 100. If I start with 50 then I get 150 in the current year, 165 the year after and 181.5 the second year after. This does not double.

If I use 75%, then I get 175 this year, 192.5 the next year and more than 200 the second year, 
the answer is in between - 65%.

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved with algebra or by TESTing THE ANSWERS. We're essentially asked to keep track of 4 years of data:

Last year 
This year 
Next year 
2 yrs from now

We're told about the percentage increases in population over the last two years (10% each), but we're asked for the percentage increase from last year to this year (with the goal that the population has to DOUBLE over the course of all of these years).

Let's make last year's population = X

Now, let's TEST Answer B….40%

Last year = X 
This year = 1.4X.... 10% of 1.4X = .14X, so....
Next year = 1.54X.... 10% of 1.54X = .154X, s....
2 years = 1.694X 
This is an increase of 69.4%, which is TOO SMALL. We need a bigger percentage increase…

Let's TEST Answer D…65%

Last year = X 
This year = 1.65X... 10% of 1.65X = .165X, so....
Next year = 1.815X... 10% of 1.815X = .1815X, so....
2 years = 1.9965X 
This is an increase of 99.65%, which is just about DOUBLE. This is a MATCH for what we're looking for.

Final Answer:  D

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

sumi747 · Answer

Current year population= 100
Next year population= 110
Next to next year population= 121= 2*population of last year
Last year population= 60.5
Therefore percentage increase of population over last year= {(100-60.5)/60.5}*100=~ 65%
IMO D

Posted from my mobile device

UserMaple5 · Answer

This question seems to be really awkwardly worded and I thought it was fairly unclear. Is this reflective of the kind of wording we can expect on the actual exam or is this more of a MGMAT special?

DhruviAg · Answer

Let the population of one year ago be "y".
Let population of this year be "x". 
Population two years from now= 2y.
Therefore, 2y=x(1.1)^2
y/x = 2/1.21 ~= 1.65
Therefore percent increase = 65%

GmatPoint · Answer

Let the population of the city be x this year and the population one year ago be y.

Population of city after 2 years = x*1.1*1.1 = 1.21*x

Also, it is given that 1.21*x = 2*y
Thus, y = 0.605x

Percentage increase over the last year = (x - 0.605x)/0.605x = 65.3%

Thus, the correct option is D.

RastogiSarthak99 · Answer

I tried algebra but due to time, I opted for numbers.

121 = 2 (x)

x = 60.5

Base yr was 100; so 100-60.5/60.5 is the percentage jump being asked for. Which is roughly 65%. D

Be careful, option B is a trap when you are in a rush.

wadhwakaran · Answer

2020- 100
2021- 110 (10% increase)
2022- 121 10% increase
2019- 2022/2= 121/2= 60.5

Change in population from 2019 to 2020 is 100-60.5= 39.5
% Change= 39.5/60.5*100= 65%

Posted from my mobile device

ManishaPrepMinds · Answer

Let's say population 1 year ago = x 
Population now = y
Population after 1 year = y × 1.1 (10% increase)=1.1y
Population after 2 years = y × 1.1 × 1.1 (another 10% increase) 1.21y
Given that population after 2 years = 2x 
1.21y = 2x
Hence ratio increase from the past year to now
y/x = 2/1.21
20/12=(12+8)/12= 1.6666
Population increase from the past year to now
1.666-1 =.666 = 66.66% 
Answer D

luisdicampo · Answer

Deconstructing the Question

Let:
 P_{-1}  = population one year ago 
 P_0  = population now 
 P_2  = population two years from now

Future growth is 10% per year for 2 years:

P_2 = P_0(1.10)^2 = 1.21P_0

We are told:

P_2 = 2P_{-1}

We want the percent increase from last year to now.

Step-by-step

Set the two expressions for  P_2  equal:

1.21P_0 = 2P_{-1}

Divide both sides by  P_{-1} :

1.21\frac{P_0}{P_{-1}} = 2

Now divide both sides by  1.21 :

\frac{P_0}{P_{-1}} = \frac{2}{1.21} \approx 1.653

165.3\% - 100\% = 65.3\%

Equivalently:

1.653 - 1 = 0.653 = 65.3\%

Answer: D

Boomtown urban planners expect the city’s population to

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Boomtown urban planners expect the city’s population to

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards