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

[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

Just to give you an alternative method, try back solving if it suits you.

I looked at the options and picked $2.00 (since it is right in the middle so even if it is not my answer, I would have eliminated 3 options after I am done with it. (I will explain you what I mean at the end.)

If largest pot cost $2, fifth largest cost 1.75, fourth largest cost 1.5 and third largest cost 1.25
The average cost of all 6 pots will be right in the middle of 1.25 and 1.5 which is 1.375 (All of this can be done in your head.)
Now all we need to do on paper is figure out 1.375 * 6 which does come out to be 8.25 (or if you like innovative ways of calculating, think that 1.25*6 is 7.5 and 1.5*6 is 9.0 so 1.375*6 must be right in the middle i.e. 8.25). Hence the largest pot must have cost $2.00
This method is very fast if you are quick in your calculations.

Here, fortunately, the first option we picked gave us the answer. It may not always happen. Say, if instead of 8.25, we get 8, we know the largest pot must have cost more so possible answers are 2.15 and 2.30. Pick either one of them and check.

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

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

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.

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!

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

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

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)

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"

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

Answer: C

We have a consecutive set of 6 flower pots. We can represent this as:
x + (x+.25) + (x+.50) + (x+.75) + (x+1) + (x+1.25) = 8.25

6x+3.75=8.25
6x=4.5
x=4.5/6

How do you quickly simplify 4.5/6?

You can realize that 7*6 = 42 and 8*6 = 48. The average of the two is 45, so the result must be between .7 and .8 or .75.

X=.75 and the largest value is 1.25+.75 or 2.00.

ans c.

Hi mathislife,

If you're actually looking to quickly simplify that fraction, then you should 'multiply out' the decimal (multiplying the numerator and denominator by 2 would be the easiest way to do that).

4.5/6 =
9/12

and then simplify that fraction...

9/12 = 3/4 = .75

GMAT assassins aren't born, they're made,
Rich

I didnt understand what formulae was taken to solve.

AP series?? a, a+d, a+2d, a+3d? whic formulae was used. Please reply

Hi Madhav1080,

There are a number of different ways that you could solve this problem; if you wanted to use a progression, then you certainly could. Since the prompt asks for the price of the LARGEST (re: most expensive) pot, then it would be most efficient to start at the largest price and work down. In that way, the 6 prices would be....

X
X - 0.25
X - 0.5
X - 0.75
X - 1.0
X - 1.25

Since the total of the 6 pots is 8.25, with a little more work, you can solve for X.

GMAT assassins aren't born, they're made,
Rich

I would consider zooming out by a factor of 25, right of the bat. 25 goes into 100 four times, so into 800 32 times, so 33 times in 825.
New (rephrased) question: if the sum of six consecutive positive integers is 33, what’s the largest of the six integers?
Solution: average must be 5.5 (ratio of sum to number of terms). So the larger 3 numbers in the set are 6, 7, and 8.
Final step: zoom back in by a factor of 25: 8*25 = 200. Answer C.

STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
Now we should give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also solve the question algebraically.
Since testing the answer choices is incredibly easy, that's what I'll do

We'll start with answer choice C ($2.00)
If the largest pot costs $2.00, then the 2nd largest pot costs $1.75, the 3rd largest pot costs $1.50, and so on.
So, if the largest pot costs $2.00, then the TOTAL cost of all six pots = $2.00 + $1.75 + $1.50 + $1.25 + $1.00 + $0.75 = $8.25. Perfect!!

Answer: C