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Assumption

by avik.ch » Mon Apr 02, 2012 7:09 am
The price of a full-fare coach ticket from Toronto to Dallas on Continental is the same today as it was a year ago, if inflation is taken into account by calculating prics in constant dollars. However, today 90 % of the Toronto to Dallas coach tickets that Continental sells are discount tickets and only 10% are full-fare tickets, whereas a year ago half were discount tickets and half were full-fare tickets. Therefore, on average, people pay less today in constant dollars for a Continental Toronto to Dallas coach ticket than they did a year ago.

Which one of the following, if assumed, would allow the conclusion above to be properly drawn?

A) A Toronto to Dallas full fare coach ticket on Continental provides ticket holders with a lower level of service today than such a ticket provided a year ago.

B) A Toronto to Dallas discount coach ticket on Continental costs about the same amount in constant dollars today as it did a year ago.

C) All full-fare coach tickets on Continental cost the same in constant dollars as they did a year ago.

D) The average number of coach passengers per flight that Continental carries from Toronto to Dallas today is higher than the average number per flight a year ago.

E) The criteria that Continental uses for permitting passengers to buy discount coach tickets on the Toronto to Dallas route are different today than they were a year ago.

[spoiler]Can't differentiate between B and D. OA is B[/spoiler]
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by sam2304 » Mon Apr 02, 2012 8:51 am
People will pay less only if everything remains same in both years - B.

Avg # ppl per flight plays no role here. Seems to be out of scope to me.
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by Bill@VeritasPrep » Mon Apr 02, 2012 8:55 am
sam2304 wrote:People will pay less only if everything remains same in both years - B.

Avg # ppl per flight plays no role here. Seems to be out of scope to me.
Exactly right. The argument focuses on average price per coach ticket, not average number of coach tickets per flight.
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by avik.ch » Mon Apr 02, 2012 8:58 am
If the average number of people increase - then does't it effect the percentage distribution ?

100 people - ---- last year :

discounted price bought : 50
full price bought : 50

1000 people ----- this year.

discounted price bought : 900
full price bought : 100.

So from here we can conclude that on average people pay less today.

Please help !!
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by sam2304 » Mon Apr 02, 2012 9:45 am
Your explanation will hold true only if B is assumed.

100 ppl. Full ticket price - 2$. Discount price 1$
50% with full ticket price = 50*2 - 100
50% with disc price = 50
Total revenue = 150/100 = 1.5$ per ticket

200 ppl
Full ticket price = 2$. Discount price may be 1.9$
90% with discnt price = 180*1.9 - 340
10% with full price = 20*2 = 40
Avg price per ticket = 380/200 = 1.9$

200 ppl
Full ticket price = 2$. Discount price may be 0.5$
90% with discnt price = 180*1 - 90
10% with full price = 20*2 = 40
Avg price per ticket = 130/200 = 0.65$

I was convinced with your explanation and was wondering earlier till I realized the catch :D.
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by killer1387 » Mon Apr 02, 2012 9:56 am
avik.ch wrote:The price of a full-fare coach ticket from Toronto to Dallas on Continental is the same today as it was a year ago, if inflation is taken into account by calculating prics in constant dollars. However, today 90 % of the Toronto to Dallas coach tickets that Continental sells are discount tickets and only 10% are full-fare tickets, whereas a year ago half were discount tickets and half were full-fare tickets. Therefore, on average, people pay less today in constant dollars for a Continental Toronto to Dallas coach ticket than they did a year ago.

Which one of the following, if assumed, would allow the conclusion above to be properly drawn?

A) A Toronto to Dallas full fare coach ticket on Continental provides ticket holders with a lower level of service today than such a ticket provided a year ago.

B) A Toronto to Dallas discount coach ticket on Continental costs about the same amount in constant dollars today as it did a year ago.

C) All full-fare coach tickets on Continental cost the same in constant dollars as they did a year ago.

D) The average number of coach passengers per flight that Continental carries from Toronto to Dallas today is higher than the average number per flight a year ago.

E) The criteria that Continental uses for permitting passengers to buy discount coach tickets on the Toronto to Dallas route are different today than they were a year ago.

[spoiler]Can't differentiate between B and D. OA is B[/spoiler]
Except B and D rest are just wrong.

now mathematically;

average for present yr < average for last yr

when you assume any variable and will proceed you will see the total number of people gets cancelled out and hence the argument as a whole remains unchanged whether you change the total number of passenger to whatever numeral.

So actually D is irrelevant to this argument.

Hope this helps..!!
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by sam2304 » Mon Apr 02, 2012 10:04 am
killer1387 wrote: when you assume any variable and will proceed you will see the total number of people gets cancelled out and hence the argument as a whole remains unchanged whether you change the total number of passenger to whatever numeral.

So actually D is irrelevant to this argument.

Hope this helps..!!
I don't think the above statement is entirely true. It do gets changed based on the discounted price. See my explanation above. Or am I misinterpreting something here ?
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by killer1387 » Mon Apr 02, 2012 11:11 pm
sam2304 wrote:
killer1387 wrote: when you assume any variable and will proceed you will see the total number of people gets cancelled out and hence the argument as a whole remains unchanged whether you change the total number of passenger to whatever numeral.

So actually D is irrelevant to this argument.

Hope this helps..!!
I don't think the above statement is entirely true. It do gets changed based on the discounted price. See my explanation above. Or am I misinterpreting something here ?
no it doesnt
check out the calculation:

D) The average number of coach passengers per flight that Continental carries from Toronto to Dallas today is higher than the average number per flight a year ago.

suppose last yr total passengers=a ; discounted price=x; full fare= y

this yr=b ; discounted price=w ; full fare= z

now as per argument its:"Therefore, on average, people pay less today in constant dollars for a Continental Toronto to Dallas coach ticket than they did a year ago. "

Conclusion:

present average < past average
=> (0.90*b*w +0.1*b*z)/b < (0.5*a*x+ 0.5*a*y)/a
=> 0.9w+0.1z < 0.5 (x+y)
-->(from this step only D is out and proved to be irrelevant as an assumption for the conclusion)

Hope it clears..!!!
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by penguinfoot » Tue Apr 03, 2012 7:40 am
The way i see it - There are 2 parts to reason :

1) Why is B the right answer ?

The assumption can be summarized as follow,
->P1: Full-Price tickets cost (Last Year) = Full-Price tickets cost(This year)
->P2: Current Year, 90% tickets sold in discount & 10% sold in Full-Charge
->P3: Last Year, 50% tickets sold in discount & 10% sold in Full-Charge
Conc : On Average, Money Generated per ticket (This Year) < Money Generated Per ticket(Last Year)

Note the terms : Average and Money Generation (Fancy work for money paid by the people who bought the ticket). You should clearly notice that the above equation can be dissected as follows :

Money Generated = Money generated by Disc tickets & Money generated by F-F tickets. Note P1 states that both FF rates , current year and last year, are the same.
The author has comfortably assumed that the discount rates available this year are equal to the discount rates of last year. Do you get where i am going ?

If the discount rates were not the same, the above equation can be proved wrong. One such example would be the following :
FF (Last year & This Year) = 100INR
Discount Last year = 50%, Discount this year = 10%
Tickets sold last year & Tickets sold last year - Does it even matter ?
The conclusion is based on the average.

2) Why is D the wrong answer ?

For three reasons, the above answer is wrong :

Mathematically : (Refer above Dissected model) It is irrelevant how many people bought the ticket, since the conclusion is based on Averages and not the Total Money Generated.

Negate Theory : The correct Assumption (AS) will bridge the gap between Premise(s) and Conclusion. The Negate of it (AS') will break the conclusion (It wont hold true).
If you negate the Choice D, it will look like this - "(D') The average number of coach passengers per flight that Continental carries from Toronto to Dallas today is not higher than the average number per flight a year ago"
My immediate response is : "So ?". This choice does not break the argument.

Stenghten ? : After re-read, the answer choice looks more as if it is Strengthening the conclusion as it directly addressed the Conclusion.

HTH!

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by avik.ch » Tue Apr 03, 2012 7:31 pm
Thank you all. My doubt is cleared now.
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by [email protected] » Thu Apr 12, 2012 9:49 pm
I think whatever doubts had, were very important. According to me, what is given in the option D needs to be calculated and then reached to a conclusion.

I calculated the option D out by the trial and error.

Whatever cases you take, i.e the figures for the past year being less or the figures for the current year being less...

The overall discounted tickets sold in the current year is any day going to be higher...

Hence you do not need to assume option D. But yes a nice question really...

I do agree with sam2304 and also thank him for a wonderful explanation...

according to the actual calculation, the price of the ticket and the price of the discounted ticked needs to remain unchanged otherwise the conclusion will not be met.

This was more of mathematical question...

Really a good question avik...
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by [email protected] » Thu Apr 12, 2012 9:58 pm
This question will really help for dealing with future similar question. Save this question somewhere and practice it.

Really a good assumption question...
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by [email protected] » Thu Apr 12, 2012 9:59 pm
This question will really help for dealing with future similar question. Save this question somewhere and practice it.

Really a good assumption question...
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by Gaurav 2013-fall » Tue Apr 17, 2012 1:14 am
did this one the quant way. and got the answer B.
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