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

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Mantrix

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24 Dec 2024, 11:23

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Please find the attached solution

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prashantthawrani

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24 Dec 2024, 11:32

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Total Animals(A)= 630

Tagged Animals(T) =(5/9)*630 =350
T=350

Untagged Animals(U) =630-350
U=280

Tagged birds, Tb= (Tb+Ub)/5..............(i)

Tm:Tb=6:1
=> Tb/T=1/7
=> Tb=T/7=350/7
=> Tb=50

From (i)
Tb= (Tb+Ub)/5
50*5=50+Ub
Ub=250-50
Ub=200

Untagged mammals,
Um=U-Ub=280-200
Um=80 (option B)

Seb2m02

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24 Dec 2024, 11:46

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I would say answer B:

Number of animals : 630
Tagged animals : 5/9x630 = 350
UnTagged animals : 630-280 = 350

Tagged bird = Birds/5
Tagged mammals = 6Birds/5
Tagged (Birds + mammals) = Birds/5 + 6Birds/5 = 350 -> Birds = 250

Tagged mammals = 6Birds/5 = (6x250)/5 -> 300

Then, untagged mammals = 380-300 = 80

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24 Dec 2024, 11:54

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IMO B

Step 1: Determine the number of tagged animals
We know that 5 out of every 9 animals are tagged. Therefore, the total number of tagged animals is:

Tagged animals=5/9×630=350

Step 2: Determine the number of untagged animals
The total number of untagged animals is:

Untagged animals=630−350=280

Step 3: Determine the number of tagged birds
We know that only a fifth of the birds are tagged. Let BB be the total number of birds. Then the number of tagged birds is:

Tagged birds=1/5B

Step 4: Determine the number of tagged mammals
Let MM be the total number of mammals. The number of tagged mammals is:

Tagged mammals=350−Tagged birds=350−1/5B

Step 5: Use the ratio of tagged mammals to tagged birds
The ratio of tagged mammals to tagged birds is 6:1. Therefore:

Tagged mammals/Tagged birds=6

Step 6: Solve for B

B=250

Step 7: Determine the number of tagged birds and mammals

Tagged birds=1/5B=1/5×250=50

Tagged mammals=350−50=300

Step 8: Determine the total number of mammals
Since the total number of animals is 630 and there are 250 birds, the number of mammals is:

M=630−250=380

Step 9: Determine the number of untagged mammals
The total number of mammals is 380, and the number of tagged mammals is 300. Therefore, the number of untagged mammals is:

Untagged mammals=380−300=80

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24 Dec 2024, 12:47

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Bunuel

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

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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We know that total animals =630.

#Total mammals = m, birds =b.
mT for tagged mammals. mN for not tagged mammals.
bT for tagged birds, bN for non tagged.

We know mT+bT =350.
mN+bN=280.

We know that mT:bT= 6:1, So mT=300, bT=50.

bT = 50, So bN=200.

So mN= 280-200=80.

IMO B

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24 Dec 2024, 12:54

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Bunuel

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	tagged	Untagged
birds	50	200	250
mams	300	80	380
	350	280	630

Hence Ans. 80

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24 Dec 2024, 13:06

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Total=630
Tagged=(5/9)*630=350, Untagged=280
Tagged Mammal=6*350/7= 300
Tagged bird=50
so total bird=50*5=250

untagged bird=250-50=200

so, untagged mammal= 280-200=80

Answer B

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24 Dec 2024, 13:19

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First we must determine how many total animals are tagged. Personally I like to just divide the 630 number by 9 and then multiple by 5 to get the 5/9 fraction of 630. This gives us 350 tagged animals.

The ratio of mammals to birds is 6:1 meaning that our "scale-up factor" for the ratio is going to be 350/7 which equals 50.

The tagged mammals equals 300 (50*6) and the tagged birds equals 50 (50*1).

We know that 1/5 of the birds have been tagged, therefore the total number of birds is 250.

If we subtract 250 from the total number of animals 630 we come up with our mammal total number of 380.

The question asks us to determine how many mammals are untagged. Therefore our last step is to subtract 300 (the determined number of tagged mammals) from the total mammal number (380).

Our final answer is B, 80 untagged mammals.

Bunuel

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satish_sahoo

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24 Dec 2024, 13:21

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Total tagged animals= $\frac{5}{9}*630=350$
Untagged= $630-350= 280$

Tagged mammals= $\frac{6}{7}*350=300$
Tagged birds= $50$
Also, $\frac{1}{5}$ of total birds are tagged, so total birds= $250$

untagged birds= $200$
untagged mammals= $280-200=80$

Hence, IMO B

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24 Dec 2024, 13:24

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IMO Answer is (B) 80

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24 Dec 2024, 13:32

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Total tagged is 5/9x630= 350. Tagged mammals 6/7x350= 300. Meaning tagged birds is 1/5x=50= x=250 (TOTAL BIRDS). Total mammals= 630-250= 380
Total tagged mammals= 350-50birds= 300 tagged mammals
Untagged mammals = 380-300= 80(B)

Bunuel

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bellsprout24

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24 Dec 2024, 18:03

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Answer is B. 80

	Tagged	Untagged	Total
Mammal	300	80	380
Bird	50	200	250
Total	350	280	630

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24 Dec 2024, 18:04

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

Karanjotsingh

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24 Dec 2024, 18:14

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1. Total Animals and Tagged Animals:

Total animals: 630
Tagged animals: 59 × 630 = 350

2. Tagged Mammals and Birds:

The ratio of tagged mammals to birds: 6:1
Let’s find out how many tagged mammals and tagged birds there are:
- Tagged mammals: 6 × 50 = 300
- Tagged birds: 1 × 50 = 50

3. Total Number of Birds:

Only a fifth of the birds are tagged:
- 1/5 × Total Birds = 50
- Total birds: 50 × 5 = 250

4. Total Number of Mammals:

Since the sanctuary has only mammals and birds:
- Total mammals: 630 − 250 = 380

5. Untagged Mammals:

Tagged mammals: 300
Untagged mammals: 380 − 300 = 80

Answer:
B. 80

AVMachine

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24 Dec 2024, 18:39

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>At a wildlife sanctuary, there are 630 animals, and 5 out of every 9 animals are tagged.

From the above statement, the total Tagged animal would be: (630/9)*5 = 350

>Of the birds, only a fifth have been tagged. Among the tagged animals, the ratio of mammals to birds is 6:1.
6x:x; Total Tagged animal 7x = 350; Birds(x) = 50; Mammals(6x) = 300
b/5 = 50; b=250; total birds are 250 then remaining must be mammals: 630-250=380;

>If the sanctuary houses only mammals and birds, how many mammals are untagged?

380-300=80

andreagonzalez2k

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24 Dec 2024, 18:49

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b=birds
m=mammals
t=tagged
u=untagged

t=5*630/9=350

bt=b/5 -> bu=4b/5
mt=6*bt=6b/5

bt+mt=t
b/5+6b/5=350
7b/5=350
b=250

b+m=630 -> m=630-250=380

mt+mu=380 -> 6*250/5+mu=380 -> mu=380-300=80

mammals untagged = 80

IMO B

MinhChau789

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24 Dec 2024, 21:50

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Let the number of birds be b, we have the following table:

	mammals	birds	Total
tagged	350-b/5	b/5	350
untagged	280 - 4b/5	4b/5	280
		b	630

Among the tagged animals, the ratio of mammals to birds is 6:1. So 350 - b/5 = 6 x (b/5)
b = 250

the number of untagged mammals = 280 - 4b/5 = 80

Answer: B

BillyButcher0956

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24 Dec 2024, 22:17

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Tagged Animals = 5/9 * 630 = 350
Untagged Animals = 280

Total Number of Birds = B = Birds who are tagged (BT) + Birds who are untagged (BU)
BT = B/5
BU = 4B/5

Let Tagged Mammals be denoted by MT and Untagged mammals by MU

So, among tagged animals (350), 6:1 is Mammals by Birds. That is, Tagged Mammals (MT) = 300 and BT = 50
If BT = 50 = B/5, then B = 250, and Untagged Birds (BU) = 200

Now, Untagged Animals = 280 = BU + MU
So, MU = 80

Bunuel

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Invincible_147

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24 Dec 2024, 22:31

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Hi All,

Given

m + b =630

--> out of 9 animals 5 are tagged= 630*(5/9)= 350 are tagged ,means 280 untagged

--> Among the tagged animals, the ratio of mammals to birds is 6:1 ,thereofore 350*(6/7) for mammals and 350*(1/7) for birds

Mammals tagged =300,

Birds tagged =50,

--> Of the birds, only a fifth have been tagged therefore (1/5)x=50, i .e x=250

Total Mammals = 630-250--> 380

Untagged mammals= 380-300-->80

Jayesh20201

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24 Dec 2024, 22:35

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Bunuel

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The challenge in the question is only in understanding what kind of a question it is. Once you have figured it is a set question, here is how I would approach it:

1: Of all animals, 5/9 are tagged, so 4/9 are untagged. Therefore ratio is 5:4. 350 Tagged and 280 Untagged
2: 1/5th of Birds are tagged. y:4y
3: For every bird tagged, there are 6 tagged mammals

Table

	Mammals	Birds	Total
Tagged	6y	y	350
Untagged		4y	280
		5y	630

Calculation:
7y=350; y=50
4y=200; untagged Mammals => 280-200=80

Therefore, select option (B)

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