The Cost of Painting a Wall Increases by a Fixed Percentage Each Year GMAT Problem Solving

Question: The cost of painting a wall increases by a fixed percentage each year. In 1970, the cost was $2,000; and in 1979, it was $3,600. What was the cost of painting in 1988?

  1. $1,111
  2. $2,111
  3. $3,600
  4. $6240
  5. $6480


Correct Answer: E

Solution and Explanation
Approach Solution 1:

It is asked to find the cost of painting in 1988 when the cost was $2,000 in 1970; and in 1979, it was $3,600 .
The Initial price of painting was 2000
1979's price of painting was 3600

Let 'x' percent be the annual increase
This means

\([1+\frac{x}{100}]^9\)*2000=36000
= \([1+\frac{x}{100}]^9\)= 1.8

So the price of painting in 1988 will be

\([1+\frac{x}{100}]^9\)* 3600

=1.8 * 3600
= 6480

The cost of painting in 1988 will be $6,480.

Approach Solution 2:
There is another approach to this question which is fairly simple
It is asked to find the cost of painting in 1988 when the cost was $2,000 in 1970; and in 1979, it was $3,600 .
because of the percentage increase Every 9 years,

This means
3600 - 2000 / 2000 * 100 = 80% change.

In the same way,
Similarly, getting a percentage change from 1979 to 1988. There is a 9-year gap. 80 percent of 3600 = 2880.
which when it is added to 3600 + 2800 will give us 6480.
The cost of painting in 1988 will be $6,480..

Approach Solution 3:

So from 1970 to 1979, the cost went up from $2,000 to $3,600 at a fixed percentage.
Letting i be the fixed percentage, this can be written as:
2000(1+i)^9=3600

Then, from 1979 to 1988, the cost went up again by the same fixed percentage. Let's call the new amount xx. This can be written as:
3600(1+i)^9= x

Now lets put both of these equation on top of eachother:
2000(1+i)^9=3600
3600(1+i)^9=x

We can divide the top equation by the bottom equation to get rid of that (1+i)^9. If that's not a technique you're comfortable with, you can also just isolate (1+i)^9, and then set up the proportion:
2000/3600=3600/x 

Simplifying:
5/9=3600/x 
5x=3600∗9
x=720∗9
x=700∗9+20∗9
x=6300+180
x=6480

“The cost of painting a wall increases by a fixed percentage each year.”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.


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