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12 Days of Christmas GMAT Competition - Day 7: At a wildlife sanctuary

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Heix

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24 Dec 2024, 22:36

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25 Dec 2024, 00:22

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First we make the matrix of the problem: Animals=Mammals+Birds here. So it takes the following situation:

5z+4z=630, 9z=630, z=70, Now we can find mammals:

So, Tagged mammals/tagged birds=6/1,
[350-x]/x=6, x=50. 280-4x=280-200=80

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25 Dec 2024, 00:51

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Total animals = 630
5 out of every 9 are tagged. We can take this as, we have groups of 9 each, and in each group 5 are tagged.

Total groups = 630/9 = 70

In each group, 5 are tagged = 70*5 = 350

Ratio of tagged mammals to tagged birds = 6:1
6x+1x = 350
7x = 350
x=50

therefore, tagged mammals 6x = 300
Tagged birds = 1x = 50

But, only B/5 were tagged, therefore, B/5 = 50
B = 250

Therefore, mammals = 630 - 250 = 380

Untagged mammals = total mammals - tagged mammals
Untagged mammals = 380 - 300 = 80

FINAL ANSWER - Option B

Bunuel

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At a wildlife sanctuary, there are 630 animals, and 5 out of every 9 animals are tagged. Of the birds, only a fifth have been tagged. Among the tagged animals, the ratio of mammals to birds is 6:1. If the sanctuary houses only mammals and birds, how many mammals are untagged?

A. 50
B. 80
C. 120
D. 200
E. 300

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25 Dec 2024, 01:03

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Ans: B

A. 50
B. 80
C. 120
D. 200
E. 300

Given: Total 630, 5 out of 9 animals are tagged = 630*(5/9) = 350 are tagged (total T)
Total UT = 630-350 = 280
among the tagged, Ratio of mammals to birds is= Mt : Bt :: 6 : 1 ==> Mt = 350*(6/7) = 300 and Bt = 50
of the birds only a 5th have been tagged = Bt = B*(1/5)= 50 this will give us B = 250
So B untagged = 250-50 = 200

	M	B	Total
T	300	50	350
UT	?=	200	280
Total		250	630

We get UT = 80

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25 Dec 2024, 01:48

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Bunuel

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The total number of animals in the sanctuary is 630. We are told that 5 out of every 9 animals are tagged. Hence, the number of tagged animals is:
Tagged animals=(5/9)×630=350
Untagged animals=630−350=280

Let M be the total number of mammals and B be the total number of birds. Since the sanctuary houses only mammals and birds, we know:
M+B=630
Among the tagged animals, the ratio of mammals to birds is 6:1. Thus, of the 350 tagged animals:

The number of tagged mammals is (6/(6+1))×350=(6/7)×350=300
The number of tagged birds is (1/7)×350=50

Only a fifth of the birds are tagged. Therefore, the total number of birds is:
Total birds=Tagged birds/(1/5)=50×5=250

Since the total number of animals is 630 and there are 250 birds, the number of mammals is:
M=630−250=380

Out of the 380 mammals, 300 are tagged. Hence, the number of untagged mammals is:
Untagged mammals=380−300=80
The number of untagged mammals is 80
Correct option: B.

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25 Dec 2024, 02:21

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Total animals: 630

Tagged animals: 5/9×630 =350

Untagged animals: 630−350 =280

Among the tagged animals, the ratio of mammals to birds is 6:1. This means:

Tagged mammals:
6/7×350 =300

Tagged birds:
1/7×350= 50

Of the birds, only a fifth have been tagged. So, the total number of birds is:

Total birds:
50×5=250

Since the sanctuary houses only mammals and birds:

Total mammals: 630−250=380

Now, we need to find the number of untagged mammals:

Untagged mammals: 380−300=80

Therefore, the number of untagged mammals is B. 80.

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25 Dec 2024, 02:31

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350 = tagged animals
300= tagged mammals, tagged birds =50
Total birds = 250
This untagged mammals = 630-350-200= 80

Ans b

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25 Dec 2024, 03:14

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At a wildlife sanctuary, there are 630 animals, and 5 out of every 9 animals are tagged. Of the birds, only a fifth have been tagged. Among the tagged animals, the ratio of mammals to birds is 6:1. If the sanctuary houses only mammals and birds, how many mammals are untagged?

5 out of every 9 animals are tagged. So, there are a total= 630/9x5= 350 tagged animals.

Among the tagged animals, the ratio of mammals to birds is 6:1. So, there are a total of 350/7x6= 300:mammals and 350/7x1= 50 birds.

Of the birds, only a fifth have been tagged. Let’s assume, there are a total of x birds, then, x/5= 50, x= 250. Which means, there are a total of 250 birds among which 200 are tagged and there. Total of 630-250= 380 mammals among which 300 are tagged. So, the untagged mammals are380-300= 80.

Answer: B. 80.

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25 Dec 2024, 03:42

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From the data:
birds/5 + 6*birds/5=350
birds=250

mammals = 630-birds = 630-250 = 380
mammals = mammals tagged + mammals untagged = 6*birds/5 + mammals untagged = 300 + mammals untagged

300 + mammals untagged = 380
mammals untagged = 80

Answer B

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25 Dec 2024, 03:53

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total animals = 630
tagged = 5/9 * 630 = 350
Tagged birds = 1/5 * total birds
Tagged Mammals / Tagged Birds = 6/1 = i.e. (350 * 6/7) & (350*1/7) = 300 & 50 respectively
50 = 1/5 * Total Birds
250 = Birds
Mammals = 630 - Birds = 630 - 250 = 380
Untagged mammals = 380 - 300 = 80

IMO B

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25 Dec 2024, 04:34

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Bunuel

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In 630 animals, 5 out of 9 are tagged. So, the ratio of Tagged to Untagged is 5:4
9x = 630; x = 70
Number of Tagged animals to Untagged = 350:280

Of the birds, 1/5th have been tagged. The ratio of Tagged to Untagged birds is 1:4

Among the tagged animals, the ratio of mammals to birds is 6:1

How many untagged mammals are there?

Ratio of tagged mammals to tagged birds = 6:1
7x = 350; x = 50
Number of tagged mammals to tagged birds = 300:50

Ratio of tagged birds to untagged birds = 1:4
If there are 50 tagged birds, then the number of untagged birds is 50 * 4 = 200

Number of untagged mammals = Number of untagged animals - Number of untagged birds
280 - 200 = 80

Type/Tag Status	Mammal	Bird	Animal
Tagged	300	50	350
Untagged	80	200	280
Total	380	250	630

[b] is the correct answer.[/b]

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25 Dec 2024, 04:50

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At a wildlife sanctuary, there are 630 animals, and 5 out of every 9 animals are tagged. Of the birds, only a fifth have been tagged. Among the tagged animals, the ratio of mammals to birds is 6:1. If the sanctuary houses only mammals and birds, how many mammals are untagged?

A. 50
B. 80
C. 120
D. 200
E. 300

For 630 animals, tagged : untagged = 5 : 4

so, tagged animals = 350
un-tagged animals = 280..............(1)

For, tagged animals (350),
mammals : birds = 6 : 1

so, tagged mammals= 300
tagged birds = 50

Since, tagged birds (1/5th of total birds); so, un-tagged birds = 200..............(2)

Un-tagged mammals = 280-200 = 80

(B) is the CORRECT answer

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25 Dec 2024, 05:34

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just make one matrix

ratio of tagged to total is 5:9 that is tagged to untagged is 5:4 by this we can calculate total tagged and untagged animals which is 350 and 280,
1/5th birds are tagged which means 4/5th birds are untagged,
and among the tagged the ratio of mammals to birds is 6:1 that is out of 350 tagged 300 are mammals and 50 are birds,
thus we can make this
T UT Total
Bird 50 200 250
Mammal 300 80 380
Total 350 280 630,
so 80 is our desired answer.

Bunuel

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25 Dec 2024, 05:38

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Total number of animals in the wildlife sanctuary is 630
5 out of every 9 animals are tagged =>
Total tagged animals = 5/9 ×630=350
Total untagged animals = 630−350=280

A fifth of the birds are tagged:

Let the number of birds be b
Tagged birds =1/5×b=0.2b
Untagged birds = b−0.2b=0.8b

Among the tagged animals, the ratio of mammals to birds is 6:1 =>

Tagged mammals = 6×(Tagged birds)=6×0.2b=1.2b
Total tagged animals = Tagged mammals + Tagged birds = 1.2b+0.2b=1.4b
=> 1.4b=350
=> b=250

Mammals = Total Animals - Birds = 630 - 250 = 380
=> Tagged Birds = 0.2b = 0.2x250 = 50
=> Tagged mammals = 350 - 50 = 300
=> Untagged mammals = Total mammals - Tagged mammals = 380-300 = 80

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25 Dec 2024, 05:44

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Bunuel

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Total Animals = 630
Tagged animals = (5/9)*630 = 350

Untagged animal = 630 - 350 = 280

M : B = 6:1 (Tagged)
M+B = 350 (tagged)

M = 300, B = 50 (tagged)

We are given only 1/5 of Birds are tagged and we know total tagged birds are 50. This makes the Total birds as 50*5 = 250.

Mammal + Birds = 630
Mammal + 250 = 630
Mammal = 380

We already know tagged mammals are 300 so, 380-300 = 80 untagged mammals.

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25 Dec 2024, 06:34

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Total no. of animals= 630
n0. of animals tagged= 630x5/9= 350
no. of animals untagged= 630-350= 280

Let no. of tagged mammals= Tm
and no. of tagged bird= Tb

So, Tm/Tb= 6/1=> [Tm=6Tb].
Tm+ Tb= 350=> 6Tb+Tb= 350=> 7Tb=350=> [Tb=50, Tm=300]

Let total no. of birds= B
and no. of Mammals= M

Given, only 1/5th of the Birds were tagged, so 1/5xB= 50=> B=250.

So, total no. of Mammals M= 630-B= 380.

So, M= 380, Tm= 300.
Therefor, no. of untagged mammals= M-Tm= 80.

Ans. opt. B (80)

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25 Dec 2024, 06:50

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Quote:

	tagged	not tagged	Total
birds	b/5	4b/5	b
mammals	m
Total	350	280	630

630 animals * 5/9 = 350 tagged animals, remaining 280 not tagged
ratio tagged mammals to birds 6:1 -> m : (b/5) = 6 : 1 -> 5m/b = 6 : 1 -> m = 6b/5. Substitute this into formula b/5 + m = 250 to solve for b = 250
-> 4b/5 = 200 -> not tagged mammals = 280 - 200 = 80

Choose B

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25 Dec 2024, 07:09

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Total animals = 630
5 out of 9 are tagged
Tagged animals = 70 * 5 = 350
6:1 = Tagged mammals : tagged birds = 300 : 50

Only 1/5th of birds are tagged
Total number of birds = 5 * 50 = 250

Total number of mammals = 380
Untagged mammals = 380 - 300 = 80

OPTION B

Bunuel

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25 Dec 2024, 07:39

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Animals tagged= 630*(5/9)=350
Out of tagged Animals Mammal : Bird=6:1 (300 :50)
Tagged Birds=50 (1/5 of Birds were tagged)
Total Birds = 50*5= 250
Mammals = Animals-Bird= 630-250 = 380
Mammals Total= 380
Mammals tagged= 300
Untagged Mammals= 80 (Ans- B)

Thanks!

Bunuel

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25 Dec 2024, 08:01

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5/9*630 =350 animals are tagged
1/5B are tagged and 4/5B are untagged

Tagged Mammals to tagged birds 6:1 and given that there's only these two types of animals we know that 6/7*350 =300 mammals tagged and 50 birds tagged

1/5B = 50, thus Birds are 250 -> untagged birds are 4/5*250 = 200

Thus untagged mammals are (630-350) - 200 =80