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percentage - DS

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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Tue Sep 20, 2016 1:34 am

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

Fiza Gupta

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Source: Beat The GMAT — Data Sufficiency | Tue Sep 20, 2016 1:34 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Sep 20, 2016 7:34 am

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,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Tue Sep 20, 2016 9:25 am

yes, will post correctly from now

Fiza Gupta

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MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Tue Sep 20, 2016 12:32 pm

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 â‰¥ 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.

Marty Murray
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MartyMurrayCoaching.com
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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Tue Sep 20, 2016 10:29 pm

Thanks Marty Murray for great explanation.

Fiza Gupta

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Sep 21, 2016 2:16 am

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.

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