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08 Jul 2016, 08:04
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(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
(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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08 Jul 2016, 10:03
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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
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
08 Jul 2016, 13:55
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Bunuel
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
