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

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Bunuel

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24 Dec 2024, 09:00

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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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Bunuel

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24 Dec 2024, 10:00

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Bunuel

This question was provided by GMAT Club
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GMAT Club's Official Explanation:

The total number of tagged animals is 630 * 5/9 = 350.
Among the tagged animals, the ratio of mammals to birds is 6:1. This means 6/7 * 350 = 300 mammals and 1/7 * 350 = 50 birds were tagged.

Since only one-fifth of the birds are tagged, the total number of birds is 50 * 5 = 250.

This makes the total number of mammals 630 - 250 = 380.

Finally, the number of untagged mammals is 380 - 300 = 80.

Answer: B.

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24 Dec 2024, 09:08

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in the sanctuary, 350, animals are tagged and 280 untagged
50 are birds and 300 are mammals among tagged
Out of birds 200 untagged
Which implies 80 mammals are untagged
Option B

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Bunuel

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Total animals = mammals + birds = 630
Tagged animals = 630*5/9 = 350
Tagged mammals = 6*350/7 = 300
Tagged birds = 350/7 = 50
Fifth of the birds are tagged, hence total birds = 5 * 50 = 250
Untagged birds = 250 - 50 = 200
Mammals untagged = Total - mammals tagged - birds tagged - birds untagged = 630 - 300 - 200 - 50 = 80

Answer: B

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24 Dec 2024, 09:10

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Total animals = 630
Tagged animals = 630 * 5/9 = 350
Birds be b, tagged birds = b/5
Ratio of mammals to tagged birds = 6:1 => tagged mammals = 6b/5
Total tagged animals = b/5 + 6b/5 = 7b/5 =350 => birds, b = 250
tagged birds = b/5 = 50, untagged birds = 4b/5 = 200, tagged mammals = 6* 250/5 = 300
Total tagged birds + tagged mammals = 250 + 300 = 550
Total untagged mammals = 630-550 = 80.
Option B

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24 Dec 2024, 09:11

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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?

	Mammals	Birds	Total
Tagged	6/7*350=300	1/7*350=50	5/9*630 = 350
Untagged	280-200=80	250-50=200	4/9*630 = 280
Total	300+80=380	50*5=250	630

The number of mammals that are untagged = 80

IMO B

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24 Dec 2024, 09:11

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There are 630 animals

5 out of 9 are tagged = 350 tagged

Among the tagged animals, mammals to Birds is 6 : 1 and we have 350 tagged
that translates to 300 mammals and 50 Birds

Of the birds, 1/5 have been tagged. which means we have 250 total birds

690 - 250 = 380 mammals

380 mammals and 300 tagged mammals equates to 80 Untagged Mammals

Answer is B: 80

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Bunuel

This question was provided by GMAT Club
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Total tagged animals: (5/9) * 630 = 350
Tagged mammals and birds: The ratio of tagged mammals to birds is 6:1. This means for every 7 tagged animals, 6 are mammals and 1 is a bird.
Tagged mammals: (6/7) * 350 = 300
Tagged birds: (1/7) * 350 = 50
Total birds: Only 1/5 of the birds are tagged. If 50 birds are tagged, then the total number of birds is 50 * 5 = 250.
Total mammals: Since the sanctuary only has mammals and birds, the total number of mammals is 630 (total animals) - 250 (total birds) = 380.
Untagged mammals: The total number of mammals is 380, and 300 of them are tagged. Therefore, the number of untagged mammals is 380 - 300 = 80.

IMO B

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24 Dec 2024, 09:15

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Understanding given classifications is the key, and then drawing the tree dig.

total animals divided into 2 groups Birds and mammals, and each type can be tagged or untagged.

There are 630 animals, and 5 out of every 9 animals are tagged.=> 5/9 of 630 = 350 animals are tagged. ------(i)
Also given among tagged animals ration of mammals:bird=6:1
Hence 300=tagged mammals and 50= tagged birds.------(ii)

Assume total birds = x
Given x/5 birds are tagged and from (ii) x/5=50
=>Total birds =250 => total mammals = 630-250 =380 {out of which 300 are tagged from (ii)

Hence untagged mammals = 380-300=80 (ans)

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Took a long time to solve!! Also, considering, I wasn't initially thinking of birds as animals. Would love to know a shortcut method for this.

My solution:
We are given total animals and ratio of tagged animals. So, Total tagged = 630 *5/9 = 350

Among the tagged animals, we know the ratio of birds and mammals. We will start with birds because we know what fraction of overall birds are tagged. Birds tagged = 1/7 *350 = 50 (using Among the tagged animals, the ratio of mammals to birds is 6:1)

Mammals tagged = 350-50= 300 (Total tagged - birds tagged)

Total birds = 50*5 = 250 (Of the birds, only a fifth have been tagged)

Total mammals = 630-250 = 380

Untagged mammals = 380-300 = 80

Bunuel

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Bunuel

This question was provided by GMAT Club
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There are 630 animals in total. 5 out of every 9 animals are tagged, so the number of tagged animals is:
630 * (5/9) = 350 tagged animals.
The number of untagged animals is:
630 - 350 = 280 untagged animals.
Among the tagged animals, the ratio of mammals to birds is 6:1. This means out of every 7 tagged animals, 6 are mammals and 1 is a bird. So:
Tagged mammals = (6/7) * 350 = 300
Tagged birds = (1/7) * 350 = 50
Only 1/5 of the birds are tagged. Let the total number of birds be x. Since 50 birds are tagged:
x / 5 = 50
x = 250
So, there are 250 birds in total.
Since the sanctuary only has mammals and birds, the total number of mammals is:
630 - 250 = 380 mammals.
Out of the 380 mammals, 300 are tagged. So, the number of untagged mammals is:
380 - 300 = 80.

Final answer: There are 80 untagged mammals.

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24 Dec 2024, 09:21

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To solve the problem, let’s break it into steps:

Step 1: Total number of animals and tagged animals
The sanctuary has 630 animals, and 5/9 of them are tagged.

Number of tagged animals= 5/9 ×630=350

This means
630−350=280 animals are untagged.

Step 2: Ratio of tagged mammals to tagged birds
The ratio of tagged mammals to tagged birds is 6:1.
Let the number of tagged mammals be 6x and the number of tagged birds be x.
The total number of tagged animals is 350:
6x+x=350
⟹ 7x=350⟹x=50
So:
Tagged mammals = 6x=6×50=300
Tagged birds = x=50

Step 3: Total number of birds and untagged birds
Among the birds, only 1/5 are tagged.
Thus, tagged birds (50) make up 1/5 of all birds:

Total birds=5×50=250
The number of untagged birds is:

Untagged birds=250−50=200

Step 4: Total number of mammals and untagged mammals
The sanctuary houses only mammals and birds. The total number of animals is 630, and there are 250 birds. Hence, the number of mammals is:

Total mammals=630−250=380
The number of tagged mammals is 300.
Therefore, the number of untagged mammals is:

Untagged mammals=380−300=80

Final Answer:
The number of untagged mammals is B. 80.

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M+B=630, Total Tagged = (5/9)630---> 350 that makes Total Untagged=280.

The ratio of Tagged Mammals to Tagged Birds=6/1--- 6X+X=7X=350-- X= 50
Tagged Birds = 50, Tagged Mammals = 300

1/5 of the total birds is 50, so total no of birds= 5*50=250. So Total number of birds=250 and Total Mammals = 380(as we know Mammals +Birds=630), We also know Untagged mammals =300 Therefore 380-300 = 80 Untagged mammals. Option B is the answer.

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24 Dec 2024, 09:23

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Total animals are 630.

Tagged animals are 5 out of 9, which is 350.

The ratio of tagged mammals to birds is 6 to 1. Solving 6x plus x equals 350 gives x equals 50.

Tagged mammals are 300 and tagged birds are 50.

Since one-fifth of birds are tagged, total birds are 5 * 50 = 250.

Total mammals are 630 - 250 = 380.

Untagged mammals are 380 - 300 = 80.

Ans. (B) - 80

	Tagged	Untagged	Total
Mammals	300	80	380
Birds	50	200	250
Total	350	280	630

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Bunuel

This question was provided by GMAT Club
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Tagged animals = 630*5/9 = 350
Untagged animals = 630*4/9 = 280

Tagged mammals = 350*6/7 = 300
Tagged birds = 50
Untagged birds = 50*4 = 200

Untagged mammals = Untagged animals - Untagged birds = 280 - 200 = 80
Answer is B

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24 Dec 2024, 09:27

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Sanctuary houses only mammals(M) and birds(B): M + B = 630 .........(1)

5 out of 9 animals are tagged,

630 = 9 * 70

Tagged animals (T) = 5 * 70 = 350

Among T, the ratio of mammals and birds is 6:1

Tagged mammals (Tm): 6 * 50 = 300
Tagged birds (Tb): 1 * 50 = 50

Of the birds only 1/5 th have been tagged: Tb = 1/5 * B
B = 250
M = 380 ......... from (1)

Untagged Mammals = M - Tm = 80

Answer B.

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24 Dec 2024, 09:32

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Total animals = 630

5/9 of total are tagged
Tagged animals = (5/9)(630) = 350
Untagged animals = 630 - 350 = 280

Among tagged animals, mammals:birds = 6:1

Let x = number of tagged birds
Then 6x = tagged mammals
7x = 350 (total tagged)
x = 50 tagged birds

Given that tagged birds = 1/5 of total birds

Total birds = 50 × 5 = 250
Total mammals = 630 - 250 = 380

Tagged mammals = 300

Untagged mammals = 380 - 300 = 80

Answer: B. 80

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24 Dec 2024, 09:33

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I think we can use a double matrix to solve

Tagged animals=5/9*630=350
Tagged(m:b=6:1) T(m)=300 T(b)=50
Total birds/5=tagged birds=50
Total birds=250

B M T
T 50 300 350
UT 200 80 280
250 380 630

So UT M is 80

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24 Dec 2024, 09:33

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The correct answer is B

	Tag	Untag	Total
Mammals	300	80	380
Birds	50	200	250
Total	350	280	630

5 out of every 9 animals are tagged,
Total animals tagged = 5/9*630 = 350
Total animals untagged = 630-350 = 280

The ratio of tagged mammals to birds is 6:1
Tagged mammals = 6/7*350 = 300
Tagged birds = 350-300 = 50

Of the birds, only a fifth have been tagged:
Let total birds be x
1/5th of x = 50
x = 250

Total mammals = 630-250 = 380

So,
Untagged mammals = 380-300 = 80
Untagged birds = 250-50 = 200

Bunuel

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24 Dec 2024, 09:34

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Total number of animals = 630
Tagged animals=5/9 * 630 = 350
Untagged animals = 630 – 350 = 280

In tagged animals, mammals : birds = 6 : 1
Let the number of tagged mammals be 6x and tagged birds be x
6x + x = 350
X = 350 / 7 = 50

Tagged mammals = 6x = 300
Tagged birds = x = 50

Only 1/5 of the birds are tagged, so:
Total birds = 5 * Tagged birds = 5 * 50 = 250

Total mammals = 630 - 250 = 380
Untagged mammals = 380 - 300 = 80