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Each member of a pack of 55 wolves has either brown or blue [#permalink]
23 Oct 2011, 09:23

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Difficulty:

95% (hard)

Question Stats:

53% (02:52) correct
47% (02:15) wrong based on 274 sessions

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a 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 to 3. (2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.

Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
17 Mar 2012, 03:28

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shadabkhaniet wrote:

Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:

Attachment:

Wolves.png [ 4.33 KiB | Viewed 3469 times ]

"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own. (2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:

Attachment:

Wolves (1)+(2).png [ 5.23 KiB | Viewed 3461 times ]

Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions: y=2 and x=7 --> 3y+7x=6+49=55; y=9 and x=4 --> 3y+7x=27+28=55; y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
17 Mar 2012, 02:43

LalaB wrote:

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a 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 to 3. (2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.

Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats" _________________

Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
17 Mar 2012, 09:13

Bunuel wrote:

shadabkhaniet wrote:

Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:

Attachment:

Wolves.png

"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own. (2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:

Attachment:

Wolves (1)+(2).png

Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions: y=2 and x=7 --> 3y+7x=6+49=55; y=9 and x=4 --> 3y+7x=27+28=55; y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
21 Aug 2013, 02:46

Bunuel wrote:

shadabkhaniet wrote:

Not able to understand the line " If there are more than 3 blue-eyed wolves with white coats"

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:

Attachment:

Wolves.png

"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own. (2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:

Attachment:

Wolves (1)+(2).png

Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions: y=2 and x=7 --> 3y+7x=6+49=55; y=9 and x=4 --> 3y+7x=27+28=55; y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Answer: C.

Hope it's clear.

There could be another solution to the equation: y=11 and x=3 --> 3y+7x=33+21=55; and in this case, 7x < 3y => A & B together are insufficient => E is the answer Am I missing something here?

Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
21 Aug 2013, 02:48

Expert's post

divineacclivity wrote:

Bunuel wrote:

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a grey coat. If there are more than 3 blue-eyed wolves with white coats, are there more blue-eyed wolves than brown-eyed wolves?

Look at the matrix below:

Attachment:

Wolves.png

"There are more than 3 blue-eyed wolves with white coats" means that # of wolves which have blue eyes AND white coats is more than 3. The question asks whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

(1) Among the blue-eyed wolves, the ratio of grey coats to white coats is 4 to 3. Not sufficient on its own. (2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1. Not sufficient on its own.

(1)+(2) When taken together we get the flowing matrix:

Attachment:

Wolves (1)+(2).png

Notice that x and y must be integers (they represent some positive multiples for the ratios given in the statements).

So, we have that 3y+7x=55. After some trial and error we can find that this equation has only 3 positive integers solutions: y=2 and x=7 --> 3y+7x=6+49=55; y=9 and x=4 --> 3y+7x=27+28=55; y=16 and x=1 --> 3y+7x=48+7=55;

Now, the third solution (x=1) is not valid, since in this case # of wolves which have blue eyes AND white coats becomes 3x=3, so not more than 3 as given in the stem. As for the first two cases, in both of them 7x is more than 3y (49>6 and 28>27), so we can answer definite YES, to the question whether there are more blue-eyed wolves (blue box) than brown-eyed wolves (brown box).

Answer: C.

Hope it's clear.

There could be another solution to the equation: y=11 and x=3 --> 3y+7x=33+21=55; and in this case, 7x < 3y => A & B together are insufficient => E is the answer Am I missing something here?

Each member of a pack of 55 wolves has either brown or blue eyes and e [#permalink]
01 Sep 2014, 09:29

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a 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 to 3. (2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.

Re: Each member of a pack of 55 wolves has either brown or blue [#permalink]
01 Sep 2014, 09:31

Expert's post

AmoyV wrote:

Each member of a pack of 55 wolves has either brown or blue eyes and either a white or a 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 to 3. (2) Among the brown-eyed wolves, the ratio of white coats to grey coats is 2 to 1.

Merging topics.

Please refer to the discussion above. _________________