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B
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Difficulty:
95%
(hard)
Question Stats:
44% (02:44) correct
56%
(02:40)
wrong
based on 136
sessions
History
Date
Time
Result
Not Attempted Yet
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 six more heavier pumpkins than lighter pumpkins.
(2) There are four times fewer lighter pumpkins than heavier ones.
(1) There are six more heavier pumpkins than lighter pumpkins.
(2) There are four times fewer lighter pumpkins than heavier ones.
29 Jul 2015, 05:58
Kudos
Bookmarks
Bunuel
IMO: B
Question Stem:
\(\frac{(10x + ry)}{(x + y)}\) = 12
10x + ry = 12x + 12y
Since value of r is asked r = \(\frac{(2x + 12y)}{y}\) --(i)
Since avg lies between min and max values
10<12<r
Thus there are y heavier pumpkins
Statement 1: There are six more heavier pumpkins than lighter pumpkins.
y = x+6
r = \(\frac{2x+ 12x+72}{x+6}\)
x is unknown
Hence not suff
Statement 2: There are four times fewer lighter pumpkins than heavier ones.
y = heavier pumpkins
then x = y/4
Sub in the eq--(i)
we get r = 12.5
Hence suff
29 Jul 2015, 06:24
Kudos
Bookmarks
Bunuel
Given : Average Weight of all Pumpkins = (10x + ry)/(x+y) = 12
i.e. (10x + ry) = 12(x+y)
i.e. (r-12)y = 2x
i.e. r = 2(x/y) + 12
So we need to calculate the value of (x/y) to calculate the value of r
Also Since Average i.e. 12 is greater than 10 therefore r must be Greater than 12 because the average liest between the bigger and smaller number
Question : Find r i.e. find (x/y) ?
Statement 1: There are six more heavier pumpkins than lighter pumpkins.
y = x+6
but (x/y) can't be calculated. Hence,
NOT SUFFICIENT
Statement 2: There are four times fewer lighter pumpkins than heavier ones.
i.e. 4x = y
i.e. (x/y) = (1/4)
i.e. r = 2(1/4)+12 = 12.5 Hence,
SUFFICIENT
Answer: option B
