yes, will post correctly from now

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

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.

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.

Thanks Marty Murray for great explanation.

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

Let the original price = $100.

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.