Confusing DS : pl help

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ankitbagla: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Sep 20, 2011 4:14 am; Thanked: 1 times

by ankitbagla » Sun Oct 20, 2013 3:48 am

Fabio's designer fashion store has become so popular that he can raise the prices every day. Each day, he raises the price of his designer pants by one dollar more than he raised it the previous day. Given that the price on Sunday the 15th was $700, what was the price on Saturday the 21st?

(1) The price on Thursday was $746.
(2) The difference between the price on Monday the 16th and Sunday the 22nd was $81.

Source : Grockit

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Source: Beat The GMAT — Data Sufficiency | Sun Oct 20, 2013 3:48 am

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 » Sun Oct 20, 2013 4:08 am

Fabio designer fashion store has become so popular that he can raise the prices every day. Each day, he raises the price of his designer pants by one dollar more than he raised it the previous day. Given that the price on Sunday the 15th was $700, what was the price on Saturday the 21st?

(1) The price on Thursday was $746.
(2) The difference between the price on Monday the 16th and Sunday the 22nd was $81.

Since the price is raised by $1 more each day, the price increases comprise a set of consecutive integers.
Given a set of consecutive integers:
Median = average = sum/number.
Sum = number * average.

The solution below presumes that statement 1 refers to Thursday the 19th.

Statement 1: The price on Thursday was $746.
Since Thursday = 746 and Sunday = 700, the sum of the increases between Sunday and Thursday = 46.
Median increase for the first 4 days = sum/number = 46/4 = 11.5.
Thus, the increase on Tuesday = $11 and the increase on Wednesday = $12.
Thus, the increases Monday through Saturday comprise the consecutive integers 10 through 15.
Sum of the increases = number * average = 6 * 12.5 = 75.
Thus, the price on Saturday = 700+75 = 775.
SUFFICIENT.

Statement 2: The difference between the price on Monday the 16th and Sunday the 22nd was 81.
Thus, the sum of the increases for the 6 days Tuesday through Sunday = 81.
Median = sum/number = 81/6 = 13.5.
Thus, the increase on Thursday = $13 and the increase on Friday = $14.
The result is the same set of consecutive integers determined in Statement 1, implying that the price on Saturday will be $775.
SUFFICIENT.

The correct answer is D.

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mevicks: Master | Next Rank: 500 Posts; Posts: 269; Joined: Thu Sep 19, 2013 12:46 amFollowed by: 7 members; Thanked: 94 times

by mevicks » Sun Oct 20, 2013 4:12 am

Hi Mitch

Would you consider it as a GMAT-like question? To me its a poorly written question that leaves out too many gaps in the logic.

Nowhere in the question its stated that we are referring to only a particular month. Many months (in different years) have Sunday the 15th.
Which Thursday it is ?
etc.

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Oct 20, 2013 4:21 am

15th = 700

To find: Price on 21st

Statement 1 :
Thursday (considering 19th) = 746
Let increment on 16th day be "a"

a + (a+1)+(a+2)+(a+3) = 746-700
4a + 6 = 46
a = 10
Now, we can find or 21st..
SUFFICIENt

Statement 2:
b + (b+1) + (b+2) + (b+3) + (b+4) + (b+5) = 81
6b + 15 = 81
b = 11
Now, we can find or 21st..
SUFFICIENt

Answer [spoiler]{D}[/spoiler]?

R A H U L

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by [email protected] » Sun Oct 20, 2013 1:28 pm

Hi mevicks,

The concepts behind this question can occur on the GMAT. However, the GMAT vets/tests its questions thoroughly before they are deemed "fair" and inserted into the pool of "active" questions, so it's highly unlikely that there will be any wording that could be considered "debatable" or confusing. This question DOES have some ambiguity to it, and as such would not appear in this format on an actual GMAT.

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Mon Oct 21, 2013 6:45 am

mevicks wrote:Hi Mitch

Would you consider it as a GMAT-like question? To me its a poorly written question that leaves out too many gaps in the logic.

Nowhere in the question its stated that we are referring to only a particular month. Many months (in different years) have Sunday the 15th.
Which Thursday it is ?
etc.

I agree; the GMAT would almost certainly specify that it's Sunday, December 15 and Saturday, December 21. Or at least specify "in the same month."

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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