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Alternative solution

by prachi18oct » Sat May 02, 2015 11:33 am
Q. each member of a pack of 55 wolves has either brown or blue eyes and either a white or grey coat. if there are more than 3 blue- eyed wolves with white coats, are there more blue-eyed Wolves than brown eyed wolves ?
(1) among the blue- eyed wolves , the ratio of grey coats to white coats is 4:3
(2) among the brown eyed wolves , the ratio of white coats to grey coats is 2:1

I approached the problem with double matrix method and eliminated option a,b,d
For c, I had to check the possible pairs of numbers valid for both the cases
Let g1 , w1 be the blue eyed wolves and g2,w2 be the brown eyed wolves
From 1, g1:w1 = 4:3 and w1 > 3 so that g1,w1 can be (8,6),(12,9),(16,12),....(28,21)
From 2 , w2+g2 should be divisible by 3. So we check cases when the sum is 55 and w2+g2/3 is integer.
By eliminating the invalid cases, we can see that there are 2 cases which satisfies all scenarios ie. When g1, w1
Are 16,12 or 28,21 the value of w2, g2 are respectively 18,9 or 4,2 .both cases blue eyed is more than brown eyed wolves
28> 27 and 49 > 6.

Is my approach correct ? Also please suggest any other pointers for quick reasoning if possible
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Source: — Data Sufficiency |
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by GMATGuruNY » Sat May 02, 2015 12:59 pm
prachi18oct wrote:Q. each member of a pack of 55 wolves has either brown or blue eyes and either a white or grey coat. if there are more than 3 blue- eyed wolves with white coats, are there more blue-eyed Wolves than brown eyed wolves ?
(1) among the blue- eyed wolves , the ratio of grey coats to white coats is 4:3
(2) among the brown eyed wolves , the ratio of white coats to grey coats is 2:1
Statement 1: Among the blue-eyed wolves, the ratio of grey coats to white coats is 4:3.
Since (blue-eyed grey):(blue-eyed white) = 4:3 -- and 4+3 = 7 -- the total number of blue-eyed wolves must be a MULTIPLE OF 7.
Since there are MORE THAN 3 blue-eyed white wolves, the least possible case is as follows:
blue-eyed grey = 8 and blue-eyed white = 6, for a total of 14 blue-eyed wolves.
No information about the number of brown-eyed wolves.
INSUFFICIENT.

Statement 2: Among the brown-eyed wolves, the ratio of white coats to grey coats is 2:1.
Since (brown-eyed white):(brown-eyed grey) = 2:1 -- and 2+1 = 3 -- the total number of brown-eyed wolves must be a MULTIPLE OF 3.
No information about the number of blue-eyed wolves.

Statements combined:
Since the number of blue-eyed wolves must be a multiple of 7 greater than or equal to 14, and the total number of wolves = 55, we get the following options:
total blue-eyed = 14, total brown-eyed = 55-14 = 41.
total blue-eyed = 21, total brown-eyed = 55-21 = 34.
total blue-eyed = 28, total brown-eyed = 55-28 = 27.

The option in red represents the least total number of blue-eyed wolves that yields a multiple of 3 for the total number of brown-eyed wolves.
Since the least total number of blue-eyed wolves (28) is more than half the total number of wolves (55), there must be MORE BLUE-EYED WOLVES THAN BROWN-EYED WOLVES.
SUFFICIENT.

The correct answer is C.
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