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

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There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each.  [#permalink]

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08 Jul 2016, 07:04
00:00

Difficulty:

75% (hard)

Question Stats:

45% (02:09) correct 55% (01:23) wrong based on 51 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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There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each.  [#permalink]

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08 Jul 2016, 09:03

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

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]

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08 Jul 2016, 12:55
1
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.

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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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18 Jul 2016, 21:10
Top Contributor
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]

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20 Feb 2018, 23:49
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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Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each.  [#permalink]

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20 Feb 2018, 23:56
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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GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each.  [#permalink]

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21 Feb 2018, 00:04
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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Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each.  [#permalink]

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21 Feb 2018, 00:07
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.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. &nbs [#permalink] 21 Feb 2018, 00:07
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