I chose A but apparently D is correct. Is there an easier way to solve the second statement?
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.
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Easier way to solve?
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To determine the ratio for the 4 years, plug in a value for the original price.Rastis wrote:I chose A but apparently D is correct. Is there an easier way to solve the second statement?
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.
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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Hi Rastis,
I like Mitch's approach to essentially TEST Values so that you can spot a hidden pattern in the math.
Depending on how you organize the information in the prompt, you can spot that same pattern using algebra. Here's how:
We're told that a property has a starting value, then the value changes each year for 3 years (note that each percentage change is based on the PRIOR YEAR'S VALUE):
Starting Value = X
Yr. 1 (+10%) = 1.1(X) = 1.1X
Yr. 2 (-20%) = .8(1.1X) = .88X
Yr. 3 (+25%) = 1.25(.88X) = 1.1X
Fact 2 can be translated into an algebra equation:
"The decrease in the value over the first two years" = .12X
"$2000 less than the increase in the third year" = .22X - 2000
.12X = .22X - 2000
At this point, we have 1 variable and 1 equation, so we CAN solve it (and get the value of X). We don't even have to do the work. If you wanted to though, you'd have....
2000 = .1X
20,000 = X
Fact 2 is SUFFICIENT
GMAT assassins aren't born, they're made,
Rich
I like Mitch's approach to essentially TEST Values so that you can spot a hidden pattern in the math.
Depending on how you organize the information in the prompt, you can spot that same pattern using algebra. Here's how:
We're told that a property has a starting value, then the value changes each year for 3 years (note that each percentage change is based on the PRIOR YEAR'S VALUE):
Starting Value = X
Yr. 1 (+10%) = 1.1(X) = 1.1X
Yr. 2 (-20%) = .8(1.1X) = .88X
Yr. 3 (+25%) = 1.25(.88X) = 1.1X
Fact 2 can be translated into an algebra equation:
"The decrease in the value over the first two years" = .12X
"$2000 less than the increase in the third year" = .22X - 2000
.12X = .22X - 2000
At this point, we have 1 variable and 1 equation, so we CAN solve it (and get the value of X). We don't even have to do the work. If you wanted to though, you'd have....
2000 = .1X
20,000 = X
Fact 2 is SUFFICIENT
GMAT assassins aren't born, they're made,
Rich
