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There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each.

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Bunuel
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There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   08 Jul 2016, 08:04
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00:00
A
B
C
D
E

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75% (hard)

Question Stats:

54% (02:33) correct 46% (02:02) wrong based on 39 sessions
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There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. The average weight of a watermelon is 12 Kg. What is the value of R?

(1) There are five heavier watermelons more than lighter watermelons.
(2) The weight of the heavier watermelons in Kg is equal to their number



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C
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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   08 Jul 2016, 10:03
Answer is C

Explanation :-
Question stem gives us \(\frac{10X+YR}{X+Y}=12\)

==>10X + YR = 12X + 12Y
2X = (R - 12)Y
So we have three variable X, Y and R to solve , we will need three equation..
we already have First equation from quesition stem

Statement 1 ) Gives us the second equation
Y=X+5 (Why is Y is the heavy watermelon? because the average weight of all watermelon is 12 , therefore there must be watermelons heavier than 10 kg, X watermelon are 10Kg therefore Y must be the heavy watermelons... )
Insufficient on its own (Option A and D out)

Statement 2) Gives us third equation
R = Y = X + 5
Insufficient on its own (Option B out)

Merging statement 1 and 2 we get three equations for three unknown hence C is sufficient

For those who want a definite proof
Merge statement 1 and 2 AND substitute for R and Y
2X = (R - 12)Y
==> 2X=(X+5-12)(X+5)
==>2X=(X-7)(X+5)

This is result in a quadratic of the the form
\(x^2 - 4x - 35 = 0.\)

Determinant is positive
b^2-4ac>0 (16-(-4*1*35) ==> two real and positive roots will be yielded by the quadratic equation.
Pick the correct one

CORRECT ANSWER C
Bunuel wrote:
There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. The average weight of a watermelon is 12 Kg. What is the value of R?

(1) There are five heavier watermelons more than lighter watermelons.
(2) The weight of the heavier watermelons in Kg is equal to their number
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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   08 Jul 2016, 13:55
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Bunuel wrote:
There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. The average weight of a watermelon is 12 Kg. What is the value of R?

(1) There are five heavier watermelons more than lighter watermelons.
(2) The weight of the heavier watermelons in Kg is equal to their number


10X+RY = 12 (X+Y)

(1) There are five heavier watermelons more than lighter watermelons.

Since Avg> 10, R >10

Y = X+5

10X + R(X+5)= 12 (X + X+5)

We have two variables in the equation. Not possible.

(2) The weight of the heavier watermelons in Kg is equal to their number
Y=R
Not sufficient as we will still have two variables.

Combining both statements

R=Y=X+5

Putting R= X+5 in 10X + R(X+5)= 12 (X + X+5) , we will get the equation with one variable. Hence, Sufficient.

C is the answer
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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   18 Jul 2016, 22:10
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It seems I am missing something here.
Is there any other quick way to solve this? I am sure, I will kill some valuable time calculating the root using the quad equation formulae. IMO, its not safe to assume that just using A and B we would find the right solution. Sometimes GMAT tricks us by giving 2 valid answers in option C.
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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   21 Feb 2018, 00:49
Bunuel wrote:
There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. The average weight of a watermelon is 12 Kg. What is the value of R?

(1) There are five heavier watermelons more than lighter watermelons.
(2) The weight of the heavier watermelons in Kg is equal to their number


Hi Bunuel

Doesn't Statement B mean that Y*R = Y or Am I missing something here. Please advise.
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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   21 Feb 2018, 00:56
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rahul16singh28 wrote:
Bunuel wrote:
There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. The average weight of a watermelon is 12 Kg. What is the value of R?

(1) There are five heavier watermelons more than lighter watermelons.
(2) The weight of the heavier watermelons in Kg is equal to their number


Hi Bunuel

Doesn't Statement B mean that Y*R = Y or Am I missing something here. Please advise.


Intending meaning is that y = r, but I agree the wording is not prices here.
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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   21 Feb 2018, 01:04
Bunuel wrote:
rahul16singh28 wrote:
Bunuel wrote:
There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. The average weight of a watermelon is 12 Kg. What is the value of R?

(1) There are five heavier watermelons more than lighter watermelons.
(2) The weight of the heavier watermelons in Kg is equal to their number


Hi Bunuel

Doesn't Statement B mean that Y*R = Y or Am I missing something here. Please advise.


Intending meaning is that y = r, but I agree the wording is not prices here.


Thanks Bunuel.

But doesn't it change the answer in this case. As, \(Y*R = Y\) --> \(Y(R-1)\) = 0 as Y can't be 0, R = 1. Please advise.
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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   21 Feb 2018, 01:07
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rahul16singh28 wrote:
But doesn't it change the answer in this case. As, \(Y*R = Y\) --> \(Y(R-1)\) = 0 as Y can't be 0, R = 1. Please advise.


Ignore this question.

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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink] New post   13 May 2019, 08:48
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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. [#permalink]
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