j_shreyans wrote: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.
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