A pumpkin patch contains x pumpkins that weigh 10 pounds each and y

Question

A pumpkin patch contains x pumpkins that weigh 10 pounds each and y pumpkins that weigh r pounds each. If the average (arithmetic mean) weight of the pumpkins is 12 pounds, what is the value of r?

(1) There are five more heavier pumpkins than lighter pumpkins.
(2) The weight in pounds of each of the heavier pumpkins is 3 more than their number.

Kudos for a correct  solution .

pacifist85 · Answer

Hello,

I don't think I have found it. But I want to be notified by the answer, so I will only post my reasoning. I will go for E.

The stem gives us this information:
x(10) + y(r) = 12 (x+y) --> just diretly moved x+y from the denominator so it is easier to read.
On the side, this also tells us that x+y are multiples of 12, even though I wasn't able to use this anywhere..

Based on the first stem, we know that the heavier pumpkins are 5 more than the lighter ones, h = l+5.
However, we don't know if r>10 or r<10. It cannot be 10 because then there wouldn't be any heavier pumkins. So, NS.

Says that the weight of the heavier pumkins is 3 more than their number.
We still don't know if r is more or less than 10 and we also don't know x and y (so the number of each type of pumkins). So, NS.

Tell us thatt the weight of the heavier pumkins is l+5+3=l+8.

What I did then is replace x+y with l+h, because it is basically the same. So, this gives:
x+y = l+h = (l+5)(l+8)+l(r).

However, we still don't know if x or y are the heavier ones. So, in the end we still end up with r, y, x and l to solve for. So, NS.

So, I think we need to know something more to solve it.

balamoon · Answer

Solution -

Average is greater than 10, it leads to r > 10.

Average --> (10x+ry)/(x+y)=12 --> r=(2x/y)+12?

Stmt1 - Given that, y=x+5.
 
r = (2x/y)+12 = (2*(y-5)/y)+12. We do not know the value of Y. Not Sufficient.

Stmt2 - Given that, r = 3+y. We do not know the value of Y. Not Sufficient.

1+2  - r = 3+y and y = x+5 --> r-3 = x+5 --> y = r-3 and x = r-8

Substitute x and y in r = (2x/y)+12 --> 2*(r-8) = (r-3)*(r-12) --> r^2-17r+52=0 --> (r-13)*(r-4) = 0 --> r =13 or 4.

The value of r = 13. Sufficient.

ANS C.

ENGRTOMBA2018 · Answer

I am critiquing your logic for statement 1. If you are given that h=l+5, you can translate it to say y=x+5 as the average of x pumpkins is 10 and the overall is 12. So x can not be the heavier ones. The heavier ones have to be 'y'. On its own, this statement is still not sufficient as :

x(10) + y(r) = 12 (x+y) and y=x+5 ---> ry = 14y+10. Still not sufficient.

Again, for your statement 2, heavier = y , lighter = x

Thus, per statement 2, r=y+3. Thus on its own, not sufficient.

Combining, you will be able to find out the value of r.

Hope this helps.

shriramvelamuri · Answer

My answer is C.

Stem:

X pumpkins weight 10 pound each->  = 10x

Y pumpking weight r pound each->   = Yr.

total weight of all pumpkins= 10x+Yr.

Average weight of all pumpins = (10x+Yr) / X+Y.

Given avg= 12.

10x+yr = 12x+ 12 Y.

=>Yr= 2x+ 12Y.- equation 1.

Option 1: There are five more heavier pumpkins than lighter pumpkins

From the stem we know that Average of X pumpkins will be 10. From the statment, as the average gone up, the average of r pumpkins must be higher.

So statement 1 can be written as y= x+5- Equation 2.

and

Statement 2 can be written as r=3+Y - Equation 3.

so either statment is not sufficient, but both are required.

Also by solving Eq2 and Eq3, we can establish a relationship between X and r and that become ours equ 4.

Hope its correct.

JJo · Answer

given: x have 10 pounds each and y have r pounds each and avg. wt is 12 pounds, hence r>10
12 = (10x+ry) / (x+y), rearranging we get r=12+2x/y or r-12=2x/y

stmt1 : y = x+5...clearly insufficient, r-12=2x/(x+5), x is unknown

stmt2 : r = 3+y...insufficient, as y is unknown

stmt1+stmt2 : from 1 we get x=y-5 & from 2 we get y=r-3

hence, x=r-3-5=r-8
now we have x&y both in terms of r, 
hence r=12+2(r-8)/(r-3)
this gives, (r-13)(r-4)=0
as r>10 (given) ...r=13

Ans. C

Bunuel · Answer

800score Official Solution:

The original statement says the average weight of a pumpkin is 12 pounds. Since x pumpkins weigh 10 pounds each, the y pumpkins must be heavier.
Writing an equation for the average weight of the pumpkins is (10x + ry) / (x + y) = 12. This equation has three unknowns.
Solve for r to get:
r = 12 + (2x/y)

Statement (1) defines the relationship between x and y as y = x + 5 or y = x – 5. Plug in the formula for r to get
r = 12 + (2(y – 5)/y)
r = 14 – 10/y
Plug in couple values of y (greater than 5) to see that they yield different results for r.
Statement (1) is not sufficient.

Statement (2) gives the relationship between y and r as r = y + 3. This isn't enough information as you can plug it into the original equation and see that too many variables remain. Plug in couple values for y to see that we get different possible valuee of r and x.

Using the given with the equations from (1) and (2), the system is
(10x + ry) / (x + y) = 12
y = x + 5
r = y + 3

Rewrite r = y + 3 as r – 3 = y.
Substitute r – 3 = y into y = x + 5 and get r – 3 = x + 5 so r = x + 8.
This gives an equation for y in terms of x, and an equation for r in terms of x.
Substitute these equations into the original equation.
(10x + ry) / (x + y) = 12. Substitute y = x + 5 and r = x + 8.
(10x + (x + 8)(x + 5)) / (x + (x + 5)) = 12
10x + (x² + 13x + 40) = 12(2x + 5)
x² + 23x + 40 = 24x + 60
x² – x – 20 = 0
(x – 5)(x + 4) = 0
x = 5 or x = -4 = 0
So there are 5 of the smaller pumpkins.
Using y = x + 5, y = 5 + 5 = 10, so there are 10 of the larger pumpkins.
And using r = y + 3, r = 13, the larger pumpkins weigh 13 pounds.

neeti041190 · Answer

For 2, why did not you consider 10=x+3?

TheKingInTheNorth · Answer

The original statement says the average weight of a pumpkin is 12 pounds. Since x pumpkins weigh 10 pounds each, the y pumpkins must be heavier.

I didn't understand this part . Please help to understand .

that if one is 10 pound and other is y pound and avg is 12 .
How can i conclude that -- y >10 taking to into account the avg 12.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

A pumpkin patch contains x pumpkins that weigh 10 pounds each and y pumpkins that weigh r pounds each. If the average (arithmetic mean) weight of the pumpkins is 12 pounds, what is the value of r?

(1) There are five more heavier pumpkins than lighter pumpkins.
(2) The weight in pounds of each of the heavier pumpkins is 3 more than their number.

In the original condition, this question is typical 2by2 question in GMAT test.

(10x+ry/x+y)=12, and thus there are 3 variables (x,y,r) and 1 equation (10x+ry/x+y)=12. We need to match the number of equations and varibles and thus we need 2 more. Since there is 1 each in 1) and 2), we need both of them and thus C is likely the answer, and it turns out that C actually is the answer.

Using both 1) & 2) together, let's start from the assumption that 10>r. x=y+5, 10=x+3, then x=7, y=2, (10*7+2r/9)=12, 70+2r=12*9=108, 2r=38, r=19. Here we assumed that pumpkin1 is more heavier, and we have contradiction.

Assuming 10<r, y=x+5, r=y+3, 10x+ry=12(x+y)=12x+12y, ry=2x+12y, r=y+3. substituting x=y-5 gives us (y+3)y=2(y-5)+12y, y^2+3y=2y-10+12y, y^2-11y+10=0, (y-10)(y-1)=0, y=10, y=1. since y=1 gives us x=-4, this is not our answer, and having y=10 gives us x=5, r=13 which is the answer.

However, solving the question directly such as the above is inappropriate for 2 minute deadline, and it's more efficient to solve through variable approach method. The answer is C.

rhine29388 · Answer

didn't understand the combine statement 1 and statement 2 part

chetan2u · Answer

Hi,
since you have asked about combined solution, i'll just speak on that..

INFO from Q- 
there are x pumpkins of 10 pounds each and y pumpkins that weigh r pounds each..
avg weight =12
so 10x+ry=12(x+y)

Info from statements 
1) y=x+5
2) r=y+3= x+5+3=x+8

Combined 
 we have all values in terms of x..
lets substitute them in 10x+ry=12(x+y).. 
so  10x + (x+8)(x+5) = 12 (x+x+5) 
=>  10x + x^2 +13x + 40 = 24x + 60 ..
 x^2 - x -20 =0 ..
 x^2 - 5x + 4x -20=0 ..
 x(x-5)+4(x-5)=0 ..
 (x-5)(x+4)=0 .
so x=5,-4 ..
x cannot be -ive so x= 5 and  r = x + 8 = 13

Hope it helps

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A pumpkin patch contains x pumpkins that weigh 10 pounds each and y

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