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Arithmetic & Goemetric Progressions ?

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by Brent@GMATPrepNow » Fri Feb 05, 2010 11:58 am
Aman verma wrote:Do they give Arithmetic or Geometric Progression questions on the actual GMAT TEST ?
For some who aren't sure about these terms, an arithmetic progression is a sequence where the terms increase or decrease by a fixed amount.
Examples: 2, 5, 8, 11, 14 . . . (each term is 3 greater than the preceding term)
7, 2, -3, -8, -13 . . . (each term is 5 less than the preceding term)

A geometric progression is a sequence where we get each term by multiplying the previous term be a fixed value.
Examples: 2, 6, 18, 54, . . . (each term is 3 times the preceding term)
Examples: 500, 50, 5, 0.5, . . . (each term is 1/10 times the preceding term)

It would be reasonable to see either type on the test BUT you would not be expected to know the terms Arithmetic Progression or Geometric Progression. The sequence would be described (for example t1 = 2 and tn = t(n-1) + 3 is one way to describe/define the sequence 2, 5, 8, 11, . . . )
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by harsh.champ » Fri Feb 05, 2010 12:04 pm
Aman verma wrote:Do they give Arithmetic or Geometric Progression questions on the actual GMAT TEST ?
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Well,it is better to practise both the types of questions.Normally you will be asked a question that tests multiple concepts along with A.P or G.P.
It will also be beneficial if you have idea about other concepts like harmonic progression etc.
Just pick any basic 11th grade math book and go through the "Series and Progressions" chapter. :)
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by Aman verma » Fri Feb 05, 2010 12:08 pm
Brent Hanneson wrote:
Aman verma wrote:Do they give Arithmetic or Geometric Progression questions on the actual GMAT TEST ?
For some who aren't sure about these terms, an arithmetic progression is a sequence where the terms increase or decrease by a fixed amount.
Examples: 2, 5, 8, 11, 14 . . . (each term is 3 greater than the preceding term)
7, 2, -3, -8, -13 . . . (each term is 5 less than the preceding term)

A geometric progression is a sequence where we get each term by multiplying the previous term be a fixed value.
Examples: 2, 6, 18, 54, . . . (each term is 3 times the preceding term)
Examples: 500, 50, 5, 0.5, . . . (each term is 1/10 times the preceding term)

It would be reasonable to see either type on the test BUT you would not be expected to know the terms Arithmetic Progression or Geometric Progression. The sequence would be described (for example t1 = 2 and tn = t(n-1) + 3 is one way to describe/define the sequence 2, 5, 8, 11, . . . )

Many Thanks to Brent . I have been wondering about this while the OG mentions that we are not suppose to know or use the formula for an Arithmetic or Geometric progressions , there are actually some questions in the OG based on A.P and G.P. Even there are some questions based on Harmonic Progressions on questions related to Time and distance.
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by Aman verma » Fri Feb 05, 2010 12:21 pm
I would like to know whether the following a Geometric Progression question ?

Q: X paid $ 9.75 for the taxi fare for his journey from airport to home. he did not paid any tip. If the cab driver charged
$ 1.00 for the 1st 1/5th mile and $ 0.40 for each subsequent 1/5th mile , what was the total distance travelled by X for the journey ?

a) 20.5

b)19.5

c)13.12

d) 9.75

e) 11.5

Please give me a solution for this problem and tell me whether this is a Geometric progression Question ?
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by harsh.champ » Fri Feb 05, 2010 12:51 pm
Aman verma wrote:I would like to know whether the following a Geometric Progression question ?

Q: X paid $ 9.75 for the taxi fare for his journey from airport to home. he did not paid any tip. If the cab driver charged
$ 1.00 for the 1st 1/5th mile and $ 0.40 for each subsequent 1/5th mile , what was the total distance travelled by X for the journey ?

a) 20.5

b)19.5

c)13.12

d) 9.75

e) 11.5

Please give me a solution for this problem and tell me whether this is a Geometric progression Question ?
_____________
Now,subtracting the charge for the 1st 1/5th mile,we get $(9.75-1)=$8.75.
Also, he paid $ 0.40 for each subsequent 1/5th mile .Let x be the no. of subsequent (1/5)th mile covered by the taxi.
{Alternatively,let 1/5th of a mile = kile(just an arbiter supposition)}
so,x * 0.4 = 8.75b
Hence,x = 21.875 kile .
Hence , total no. of miles = (1/5) + (21.875/5) = 4.575 which is not any of the answer choices.
Also,what is the unit of the answer choices?Is it miles??
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by Stuart@KaplanGMAT » Fri Feb 05, 2010 1:01 pm
Aman verma wrote:I would like to know whether the following a Geometric Progression question ?

Q: X paid $ 9.75 for the taxi fare for his journey from airport to home. he did not paid any tip. If the cab driver charged
$ 1.00 for the 1st 1/5th mile and $ 0.40 for each subsequent 1/5th mile , what was the total distance travelled by X for the journey ?

a) 20.5

b)19.5

c)13.12

d) 9.75

e) 11.5

Please give me a solution for this problem and tell me whether this is a Geometric progression Question ?
This is a great example of a progression question that you can answer even if you have no knowledge of progressions.

To solve, we'd simply work our way through the problem:

$9.75 total, minus $1.00 for the first .2 miles leaves us with $8.75.

$8.75/$.40 = bit more than 21 tells us the mileage for the rest of the journey.

Only choice (A) is more than 20, so we confidently pick it without doing any further calculations. If we needed to be more precise, the answer would be:

8.75/.40 + .2

(which, as harsh.champ notes, isn't one of the choices, so there's an error in the question somewhere).

* * *

Regarding more formal progression questions (we often call them sequence questions), they're fairly rare on the GMAT. Learn to understand the definitions that you're given and how they work, but you don't need to spend a lot of time worrying about them.
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by harsh.champ » Fri Feb 05, 2010 1:17 pm
Stuart Kovinsky wrote:
Aman verma wrote:I would like to know whether the following a Geometric Progression question ?

Q: X paid $ 9.75 for the taxi fare for his journey from airport to home. he did not paid any tip. If the cab driver charged
$ 1.00 for the 1st 1/5th mile and $ 0.40 for each subsequent 1/5th mile , what was the total distance travelled by X for the journey ?

a) 20.5

b)19.5

c)13.12

d) 9.75

e) 11.5

Please give me a solution for this problem and tell me whether this is a Geometric progression Question ?
This is a great example of a progression question that you can answer even if you have no knowledge of progressions.

To solve, we'd simply work our way through the problem:

$9.75 total, minus $1.00 for the first .2 miles leaves us with $8.75.

$8.75/$.40 = bit more than 21 tells us the mileage for the rest of the journey.

Only choice (A) is more than 20, so we confidently pick it without doing any further calculations. If we needed to be more precise, the answer would be:

8.75/.40 + .2

(which, as harsh.champ notes, isn't one of the choices, so there's an error in the question somewhere).

* * *

Regarding more formal progression questions (we often call them sequence questions), they're fairly rare on the GMAT. Learn to understand the definitions that you're given and how they work, but you don't need to spend a lot of time worrying about them.
___________________
Hey Stuart,
I think over here you fell into one of the question traps
.In the question it is written that $ 1.00 for the 1st 1/5th mile and $ 0.40 for each subsequent 1/5th mile.I think you have solved the question considering the following statement:$ 1.00 for the 1st 1/5th mile(over here you have considered) and $ 0.40 for each subsequent mile(over here you missed out).
$8.75/$.40 = bit more than 21 tells us the mileage for the rest of the journey.

Only choice (A) is more than 20, so we confidently pick it without doing any further calculations. If we needed to be more precise, the answer would be:

8.75/.40 + .2
I think the answer will be (8.75/0.40)*0.2 + 0.2
What-say?? :)

Even still,no answer choice matches with the solution.I guess some typo error or wrong answer choices in the question.
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by Stuart@KaplanGMAT » Fri Feb 05, 2010 3:05 pm
harsh.champ wrote:
___________________
Hey Stuart,
I think over here you fell into one of the question traps
.In the question it is written that $ 1.00 for the 1st 1/5th mile and $ 0.40 for each subsequent 1/5th mile.I think you have solved the question considering the following statement:$ 1.00 for the 1st 1/5th mile(over here you have considered) and $ 0.40 for each subsequent mile(over here you missed out).
$8.75/$.40 = bit more than 21 tells us the mileage for the rest of the journey.

Only choice (A) is more than 20, so we confidently pick it without doing any further calculations. If we needed to be more precise, the answer would be:

8.75/.40 + .2
I think the answer will be (8.75/0.40)*0.2 + 0.2
What-say?? :)

Even still,no answer choice matches with the solution.I guess some typo error or wrong answer choices in the question.
You're right! I calculated miles rather than .2s of a mile. You're also right in that there's no answer even close to the right one, which is just over 4.5 miles.

We also could have made the math easier by just converting to miles, since the answers are so far apart:

40 cents for each 1/5 of a mile = 2.00 for each mile; 8.75/2 = 4.375, 4.375 + .2 = 4.575 miles total.
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by harsh.champ » Fri Feb 05, 2010 10:58 pm
Stuart Kovinsky wrote:
harsh.champ wrote:
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You're right! I calculated miles rather than .2s of a mile. You're also right in that there's no answer even close to the right one, which is just over 4.5 miles.

We also could have made the math easier by just converting to miles, since the answers are so far apart:

40 cents for each 1/5 of a mile = 2.00 for each mile; 8.75/2 = 4.375, 4.375 + .2 = 4.575 miles total.
That's why I took a new variable kile for my convenience.
In questions like these,where I find that the test-setter want us to fall in some trap,I like to assign some single variable to any set of complex variables.[ Over here, it was quite simple:1/5th of a mile = kile ,but in some situations you can be faced with complex variables [like in one of my post,Ian Stewart(an instructor) had suggested replacing 1/x=a , 1/y=b , 1/z=c https://www.beatthegmat.com/one-of-the-t ... 51647.html ]
I find that by applying such arbiter suppositions,the question appears quite simple.Moreover, solving the equations also seems easy and less cumbersome.
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by Aman verma » Sat Feb 06, 2010 1:18 am
First of all I would like to thank everybody to have participated in the quiz and provided their invaluable views. I hope you all will continue to help me and guide me through my queries.

Now, regarding the answer choices they are 100% accurate. Even I was bit confused at the outset as none of my answers reached above 6. So the most plausible solution to this problem is :

This is an Infinite geometric progression series Question :

Let the total distance be x miles.Then 1/5.x = First 1/5th mile

Now 1+ (x/5)(0.4)+(0.4)^2.(x/5)+....................... =9.75

1 + 0.4(x/5)[ 1 +0.4+ (0.4)^2+.........................] = 9.75

1+ 0.40(x/5)[ 1/(1-0.4)] = 9.75 Formula for infinite G.P [ a/(1-r) ]


1 +2/3.x=9.75

x= 13.12 [ approximately]

This is the closest answer I am able to come up with.If anybody feels otherwise please give their valuable comments on this.
Last edited by Aman verma on Sat Feb 06, 2010 2:03 am, edited 1 time in total.
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Wrong Interpretation

by harsh.champ » Sat Feb 06, 2010 1:43 am
Aman verma wrote:First of all I would like to thank everybody to have participated in the quiz and provided their invaluable views. I hope you all will continue to help me and guide me through my queries.

Now, regarding the answer choices they are 100% accurate. Even I was bit confused at the outset as none of my answers reached above 6. So the most plausible solution to this problem is :

This is an Infinite geometric progression series Question :

Let the total distance be x miles.Then 1/5.x = First 1/5th mile

Now 1+ (x/5)(0.4)+(0.4)^2.(x/5)+....................... =9.75

1 + 0.4(x/5)[ 1 + (0.4)^2+.........................] = 9.75

1+ 0.40(x/5)[ 1/(1-0.4)] = 9.75 Formula for infinite G.P [ a/(1-r) ]


1 +2/3.x=9.75

x= 13.12 [ approximately]

This is the closest answer I am able to come up with.If anybody feels otherwise please give their valuable comments on this.
Hey Aman,
Check the line I have bold-faced above.Now,look carefully at the red portion.
According to you for the 2nd subsequent (1/5)th of a mile,he will charge 0.4^2.
Now,it should be 0.4 only ,not 0.4^2.Just think it out practically,the normal autos also work on the same formula as described in the question.
And thus for the subsequent any number of 1/5th mile,it will not be 0.4^2,0.4^3.......... Just plain 0.4.


On a different note,suppose the equations that you have formulated is correct:-
Now 1+ (x/5)(0.4)+(0.4)^2.(x/5)+....................... =9.75 ----------{line 1}

1 + 0.4(x/5)[ 1 + (0.4)^2+.........................] = 9.75 ----------{line 2}


Moving from 1st to 2nd line,the 2nd term of the series will be 0.4 not 0.4^2.
Just keep in mind.These type of errors can happen in examination circumstances and can hamper your score.
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by Aman verma » Sat Feb 06, 2010 2:16 am
I have made the small correction pointed out.
Now in an infinite geometric series the series goes on like this :
a+ ar+ ar^2..................................... . And if anybody notice carefully , the question do lend itself to an infinite Geometric series in which case it do works as given above a+ ar+ ar^2.............................. .Please observe the structure of the question ;it do appears to be a fit case for an infinite geometric series.

However, if anybody feels otherwise please provide an explanation of his/her views
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by harsh.champ » Sat Feb 06, 2010 3:47 am
Aman verma wrote:I have made the small correction pointed out.
Now in an infinite geometric series the series goes on like this :
a+ ar+ ar^2..................................... . And if anybody notice carefully , the question do lend itself to an infinite Geometric series in which case it do works as given above a+ ar+ ar^2.............................. .Please observe the structure of the question ;it do appears to be a fit case for an infinite geometric series.

However, if anybody feels otherwise please provide an explanation of his/her views
_______________
Well,I surely feel otherwise.
The question is not that of a geometric series.

Please read this soln. posted by me:-
Hey Aman,
Check the line I have bold-faced above.Now,look carefully at the red portion.
According to you for the 2nd subsequent (1/5)th of a mile,he will charge 0.4^2.
Now,it should be 0.4 only ,not 0.4^2.Just think it out practically,the normal autos also work on the same formula as described in the question.
And thus for the subsequent any number of 1/5th mile,it will not be 0.4^2,0.4^3.......... Just plain 0.4.
It is definitely not a G.P.
Just read the question carefully,note what is being asked and you will understand the point made by me before hand .
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by Ian Stewart » Sat Feb 06, 2010 6:14 am
Aman verma wrote:
Now, regarding the answer choices they are 100% accurate. Even I was bit confused at the outset as none of my answers reached above 6. So the most plausible solution to this problem is :

This is an Infinite geometric progression series Question :
Perhaps the question designer intended for this to be a geometric series question, but as it's worded, it certainly is not. There is nothing in the wording of the question to suggest any relationship with geometric series (there is nothing to suggest we should be multiplying the 0.4 values); the only reasonable interpretation is the one used by Stuart in his solution above. If the question designer meant for this to be about geometric series, he or she needs to rewrite the question!
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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