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Mark bought a set of 6 flower pots of different sizes at a

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Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post Updated on: 30 Oct 2012, 02:17
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Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

A. $1.75
B. $1.85
C. $2.00
D. $2.15
E. $2.30

Originally posted by Poots on 14 Oct 2008, 17:21.
Last edited by Bunuel on 30 Oct 2012, 02:17, edited 2 times in total.
Renamed the topic and edited the question. Moved to PS forum.
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 30 Oct 2012, 02:27
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Poots wrote:
Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

A. $1.75
B. $1.85
C. $2.00
D. $2.15
E. $2.30


Notice that the prices are are evenly spaced, with common difference of 0.25. Now, for every evenly spaced set (average)=(first+last)/2=(sum)/(number of terms).

Now, if we say that the price of the largest pot is $x, then the price of the smallest pot is $(x-5*0.25) and we'll have that \(\frac{x+x-1.25}{2}=\frac{8.25}{6}\) --> \(2x-1.25=\frac{8.25}{3}\) --> \(x=2\).

Answer: C.
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Re: Applied Problem???  [#permalink]

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New post 14 Oct 2008, 17:29
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2
C

6x+.25+.5+.75+1.0+1.25 = 8.25
6x = 4.5
x = .75

Largest is x +1.25 = 2.00
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Re: Applied Problem???  [#permalink]

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New post 15 Oct 2008, 02:51
1
[quote="Poots"]Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

A. $1.75
B. $1.85
C. $2.00
D. $2.15
E. $2.30

x+(x+0.25)+(x+2*0.25)........

6x+0.25*15 = 8.25

x = 0.75, largest pot = 0.75+0.25*5 = 2.00....c
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 30 Oct 2012, 02:03
1
x denotes for the price of the largest pot

x + (x - 0.25) + (x-2*0.25) + ...... (x -5*0.25) = 8.25
6x - 0.25*(1 +2.+3+4+5) = 8.25
6x -3.75 = 8.25
6x = 12
x = 2

=> C is corect answer
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 25 Oct 2013, 23:09
2
Poots wrote:
Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

A. $1.75
B. $1.85
C. $2.00
D. $2.15
E. $2.30


Sum = Avg x n
8.25 = (x1 + x6)/2 X 6
x1 + x6 = 2.75------1

x6 = x1 + 5X0.25------2

solving 1 & 2
x6 = 2.00
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 06 Jan 2014, 05:42
1
Hi Brunel,
If i say price of smallest pot be x ,then price of largest pot will be x+ 5(0.25)=x+1.25
Now,if i put this in (average)=(first+last)/2=(sum)/(number of terms).

I will get the other equation:
x+1.25+x
----------- = 8.25
2 ------
6
and this will give a different answer.
Can you please explain if i am doing anything wrong here?[quote][/quote]
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 06 Jan 2014, 09:07
2
Poots wrote:
Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

A. $1.75
B. $1.85
C. $2.00
D. $2.15
E. $2.30


Instead of using the equation, lets use some common sense.
8.25/6 = 1.4XX (approx)
Now as there are 6 items , 1.4XX should be between 3rd pot cost and 4th pot cost.
Take the simplest option to verify, option c)
if 6th pot is 2.00, 5th should 1.75, 4th should be 1.5 and 3rd should be 1.25. 1.5 + 1.25 comes to 1.42 close to previously calculated.
Just to be sure, lets take 2.15, then 4th pot should be 1.65 and 3rd pot should be 1.4, average of 3rd and 4th > 1.4. Option C)

if GMAT gives options why not use it. :-D
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Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 21 Mar 2015, 07:36
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The most easiest way to approach this problem is
let x be the largest pot then

x+(x-$.25)[5th pot]+(x-$.50)[4th pot]+(x-$.75)[3rd pot]+(x-$1)[2nd pot]+(x+-1.25)[1st pot] = $8.25
6x - $3.75 = $8.25
6x= $8.25+$3.75
6x = $12
x=$2 Boom!
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 21 Mar 2015, 11:57
1
Hi All,

This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.

We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.

Since the total price is $8.25 (a 25-cent increment) and the the difference in sequential prices of the pots is 25 cents, the largest pot PROBABLY has a price that is a 25-cent increment. From the answer choices, I would then TEST Answer C first (since answers B and D are NOT in 25-cent increments).

IF....
The largest pot = $2.00
The other 5 pots are....
1.75
1.50
1.25
1.00
0.75
Total = $8.25
So this MUST be the answer.

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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 10 Nov 2016, 11:12
1
Poots wrote:
Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

A. $1.75
B. $1.85
C. $2.00
D. $2.15
E. $2.30



Well do have a formulae for the Sum of the numbers in A.P
Sn= n[2a + (n-1)d] / 2
where Sn=sum of the numbers in AP
a = fist term (over here assume to be "x")
n= numbers of terms (over here it is 6)
d= common difference (over here it is 0.25)

Equating "x" we'll get as x=first term = 0.75
so highest term or the last term = 2.0 :)
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 13 Jun 2018, 23:44
Poots wrote:
Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

A. $1.75
B. $1.85
C. $2.00
D. $2.15
E. $2.30


Responding to a pm:

There are few terms and calculations are quite simple. I will simply say that x is the cost of the largest pot and cost of subsequent smaller pots will be x - .25, x - .5 etc. So there will be 6 x's and 5 terms of -.25, -.5, -.75, -1, -1.25 which add up to -3.75

8.25 = 6x - 3.75
x = 2

Answer (C)
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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New post 23 Jun 2018, 11:29
1
Find the value of x1 first:

Question:

x1 + x2 + x3 + x4 + x5 + x6 = 8.25

Then we have:

x + (x + 0.25) + (x + 0.5) + (x + 0.75) + (x + 1) + (x + 1.25) = 8.25

We can re-write it like this:

x + x + 0.25 + x + 0.5 + x + 0.75 + x + 1 + x + 1.25 = 8.25

we get:
6x + 3.75 = 8.25 ====> 6x = 8.25 - 3.75 ====> 6x = 4.5 ====> x1 = 4.5/6 = 0.75 ===>Therefore x1 = 0.75

now the rest of the pots: x2, x3....x6 = 5*0.25 = 1.25. Now we sum both x1 + (x2,x3...x6) where x1 = 0.75 and the (x2,x3...x6) = 1.25

therefore 0.75 + 1.25 = 2. Hence answer is "C"
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