Property price

[j_shreyans]

The price of a certain property increased by 10% in the first year, decreased by 20% in the second year, and increased by 25% in the third year. What was the amount of the dollar decrease in the property price during the second year?

(1) The price of the property at the end of the third year was $22,000.

(2) The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.

OAD

I need to understand the statement 2.

Please advise

[GMATGuruNY]

The price of a certain property increased by 10% in the first year, decreased by 20% in the second year, and increased by 25% in the third year. What was the amount of the dollar decrease in the property price during the second year?

(1) The price of the property at the end of the third year was $22,000.

(2) The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.

OAD

I need to understand the statement 2.

Please advise

To determine the ratio for the 4 years, plug in a value for the original price.

Since 10% = 1/10, 20% = 1/5, and 25% = 1/4, let the original price = the product of the 3 denominators = 10*5*4 = 200.
If the original price = 200, we get:

1st-year price = 200 + 10% of 200 = 200+20 = 220.
2nd-year price = 220 - 20% of 220 = 220-44 = 176.
3rd-year price = 176 + 25% of 176 = 176+44 = 220.

Resulting ratio:
original : 1st year : 2nd year : 3rd year = 200 : 220 : 176 : 220.

Statement 1: The price of the property at the end of the third year was $22,000.
Since original : 1st year : 2nd year : 3rd year = 200 : 220 : 176 : 220, and the actual price in the 3rd year = 22000, all of the parts of the ratio must be multiplied by a FACTOR OF 100:
original : 1st year : 2nd year : 3rd year = 20000 : 22000 : 17600 : 22000.
Thus:
Decrease in the second year = 1st year - 2nd year = 22000-17600 = 4400.
SUFFICIENT.

Statement 2: The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.
The values implied by statement 1 -- 20000 : 22000 : 17600 : 22000 -- also satisfy statement 2:
Decrease over the first 2 years = original - 2nd year = 20000 - 17600 = 2400.
Increase in the 3rd year = 3rd year - 2nd year = 22000 - 17600 = 4400.
Difference = 4400-2400 = 2000.

Thus, statement 2 requires the same values as statement 1, implying that the decrease in the second year = 4400.
SUFFICIENT.

The correct answer is D.

[Jim@StratusPrep]

If you think of percentages as 'relative relationships' you can stay away from the calculation on a problem like this. If you were to do the calculations, you would see that the absolute difference between different sets of numbers will change. Percentages applied to smaller numbers have a smaller nominal change (absolute change) than the same percentages applied to bigger number. Thus, if the absolute difference between 2 specific percentages is identified, there can only be one set of relative numbers that can produce this absolute difference.


I know that is a mouthful and a little technical, but read it carefully.

[DavidG@VeritasPrep]

The price of a certain property increased by 10% in the first year, decreased by 20% in the second year, and increased by 25% in the third year. What was the amount of the dollar decrease in the property price during the second year?

(1) The price of the property at the end of the third year was $22,000.

(2) The decrease in the property price over the first two years was $2,000 less than the increase in the property price during the third year.

I need to understand the statement 2.

Algebraically, we can set it up like this:
Start: x
End Year 1: 1.1x
End Year 2: (1.1x) *(.8) = .88x
End Year 3: .88x * 1.25 = 1.1x

Note that if we find a value for x, we can find the value of every time period.

S2 tell us that the decrease over the first 2 years was $2000 less than the increase during the third year. The moment you realize that it's possible to assemble a single linear equation with one variable, you know it's possible to solve for x, and the statement is sufficient.

But, for fun, we'll make the equation.

The decrease over the first two years would be the difference between the initial value and the value at the end of year 2, or = x - .88x = .12x

The increase in the third year is the difference between the end of the second year and the end of the third, or 1.1x - .88x = .22x

We're told that the first expression is 2000 less than the second, or .12x = .22x - 2000. Again, we can obviously solve this for x, but we'll get .10x = 2000, or x = 20,000. You could then plug in this value for x to solve for any period.

[nikhilgmat31]

Answer is D

we can solve it by taking 1.10 * .80 * 1.25 x as the price at end of three years.