If a price was increased by x% and then decreased by Y%, is the new price is higher than the original?
(I) x> y
(II) x = 1.2y
percentage - DS
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- fiza gupta
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From now on, you should post math questions in their correct forums:
Problem Solving: https://www.beatthegmat.com/problem-solving-f6.html
Data Sufficiency: https://www.beatthegmat.com/data-sufficiency-f7.html
Cheers,
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Problem Solving: https://www.beatthegmat.com/problem-solving-f6.html
Data Sufficiency: https://www.beatthegmat.com/data-sufficiency-f7.html
Cheers,
Brent
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Notice: Statement 1 and Statement 2 can be tested at the same time, since as long as x > y > 0, then if x = 1.2y, then x > y.fiza gupta wrote:If a price was increased by x% and then decreased by Y%, is the new price is higher than the original?
(I) x > y
(II) x = 1.2y
Statement 1:
Since x > y, the new price could be greater than the old price as x could be any number and y could be 0.
So the key to assessing Statement 1 is determining whether the new price could be lower than the old price.
Notice the following.
x is a percentage of a lower base.
y is a percentage of a higher base.
So if x = y, the decrease would be greater than the increase.
Example:
x = y = 20
Original Price: P
Price After Increase: 1.2 P
New Price: 1.2P * .80 = .96P
So even though x = y, New Price < Original Price
New Price can also be less than Original Price when x > y.
Try x = 60 and y = 50. 60 = 1.2 * 50. So these numbers will work for Statement 2 also.
Original Price: P
Price After Increase: 1.60P
New Price: 1.60P * 0.50 = .80P
New Price < Old Price
Two different answers.
Insufficient.
Statement 2:
If x and y are both relatively low, we may get a result different from the one we get when y ≥ 50.
Try x = 12 and y = 10.
Original Price: P
Price After Increase: 1.12P
New Price: 1.12P * .9 = 1.008P
New Price > Original Price
Since x = 50 and y = 60 and x = 12 and y = 10 fit both statements, we have two different answers for Statement 1, two for Statement 2 and two for the statements combined.
Insufficient.
The correct answer is E.
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Let the original price = $100.fiza gupta wrote:If a price was increased by x% and then decreased by Y%, is the new price is higher than the original?
(I) x> y
(II) x = 1.2y
Statement 2:
Case 1: y=10, implying that x=12
Price increased by 12% = 100 + (12% of 100) = 100 + 12 = 112.
New price after a 10% decrease = 112 - (10% of 112) = 112 - 11.2 = 100.8.
In this case, the new price is higher than the original price, so the answer to the question stem is YES.
Case 2: y=100, implying that x=120
In this case, the price increases by 120% and then decreases 100% to yield a new price of $0.
Thus, the new price is lower than the original price, so the answer to the question stem is NO.
Cases 1 and 2 satisfy both statements.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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