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Intern  Joined: 25 Aug 2008
Posts: 30
Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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24 00:00

Difficulty:   45% (medium)

Question Stats: 71% (02:21) correct 29% (02:34) wrong based on 526 sessions

### HideShow timer Statistics 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.
Math Expert V
Joined: 02 Sep 2009
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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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 $$\frac{x+x-1.25}{2}=\frac{8.25}{6}$$ --> $$2x-1.25=\frac{8.25}{3}$$ --> $$x=2$$.

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3
C

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

Largest is x +1.25 = 2.00
##### General Discussion
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[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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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

Manager  Joined: 01 Jan 2013
Posts: 50
Location: India
Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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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

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
Intern  Joined: 07 Jul 2012
Posts: 2
Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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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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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. _________________
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Kinjal

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Intern  Joined: 21 Feb 2015
Posts: 26
Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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6
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! EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14567 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Mark bought a set of 6 flower pots of different sizes at a [#permalink] ### Show Tags 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. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
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Intern  Joined: 30 Apr 2015
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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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

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 Veritas Prep GMAT Instructor D
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Location: Pune, India
Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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1
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

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

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

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2
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"
Intern  B
Joined: 21 Nov 2018
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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kinjiGC wrote:
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. 8.25/6 is equal to 1.375 instead of 1.4..
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Re: Mark bought a set of 6 flower pots of different sizes at a  [#permalink]

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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

We can let the cost of the largest (or most expensive) pot be n and create the equation:

n + (n - 0.25) + (n - 0.5) + (n - 0.75) + (n - 1) + (n - 1.25) = 8.25

6n - 3.75 = 8.25

6n = 12

n = 2

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