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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head 14 Apr 2019, 23:55
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D
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89% (01:38) correct 11% (01:58) wrong based on 44 sessions

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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head count of the two species together is 12, and the leg count is 32. How many pigeons and how many rabbits are there in the zoo?

(A) 4, 8
(B) 6, 6
(C) 6, 8
(D) 8, 4
(E) 8, 6
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D
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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head 15 Apr 2019, 00:04
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Solution 1 (using 1 variable)


Given:
    • In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs.
    • The head count of the two species together is 12, and the leg count is 32.

To find:
    • The individual number of pigeons and rabbits.

Approach and Working:
Let us assume the number of pigeons is n.
    • As total number of pigeons and rabbits in 12, number of rabbits = 12 – n

Total leg count for pigeons = 2n
Total leg count for rabbits = 4(12 – n) = 48 – 4n

Therefore, we can write
    • 2n + 48 – 4n = 32
    Or, 2n = 16
    Or, n = 8

Hence, number of pigeons = 8

Therefore, number of rabbits = (12 – 8) = 4

Hence, the correct answer is option D.

Answer: D

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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head 15 Apr 2019, 00:09
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Solution 2 (using 2 variables)


Given:
    • In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs.
    • The head count of the two species together is 12, and the leg count is 32.

To find:
    • The individual number of pigeons and rabbits.

Approach and Working:
Let us assume the number of pigeons and rabbits are p and r respectively.
    • As total number of pigeons and rabbits in 12, p + r = 12… (1)

Total leg count for pigeons = 2p
Total leg count for rabbits = 4r
    • Therefore, we can write 2p + 4r = 32
    Or, p + 2r = 16… (2)

Solving equation (1) and (2), we get
    • p = 8 and r = 4

Hence, the correct answer is option D.

Answer: D

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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head 15 Apr 2019, 00:13
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x+y=12...(1)
2x+4y=32...(2)

From eqation (1) & (2)
x=8, y=4
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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head 15 Apr 2019, 00:17
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Solution 3 (without using any variable)


Given:
    • In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs.
    • The head count of the two species together is 12, and the leg count is 32.

To find:
    • The individual number of pigeons and rabbits.

Approach and Working:
Let us assume that all the 12 animals are pigeons.
Hence, the total number of leg count should have been 12 x 2 = 24.
    • But in reality, the total leg count is 32.
    • The difference of 32 – 24 = 8 happened because some rabbits are assumed to be pigeons

For 1 such instance, the difference is (4 – 2) = 2.
    • Therefore, to create a difference of 8, we need 8/2 = 4 rabbits
    • And the remaining 12 – 4 = 8 animals are pigeons
Hence, the correct answer is option D.

Answer: D

Note: We can solve it assuming all animals as rabbits also.

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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head 15 Apr 2019, 00:50
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We can use answer choices directly.

Given - Head count of the two species together is 12.

So we will select those answers that add up to 12. only A B and D.

(A) 4, 8
(B) 6, 6
(D) 8, 4

Now , each pigeon has - 2 legs and each rabbit has 4 legs.

A - 4 , 8 => 4 * 2 + 8 * 4 = 8+32 = 40 legs , but in question we are told total legs are - 32 . So wrong.
B - 6 , 6 => 6* 2 + 6 * 4 = 12+ 24 = 36 legs , Wrong.
D - 8 , 4 => 8 * 2 + 4 * 4 = 16+16 = 32. Correct.

So the answer is D.

Thanks - C.
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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head 15 Apr 2019, 01:27
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Answer is D.

The total legs are 32 so we can start testing with 8 Rabbits, 6 Rabbits, 4 Rabbits
=> Answer is D because if 8 rabbits => 32 legs but no pigeons. If 6 rabbits => 4 pigeons, total head = 10. If 4 rabbits => 8 pigeons, total head = 12.
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In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head 15 Apr 2019, 01:55
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Bunuel
In a zoo, each pigeon has 2 legs, and each rabbit has 4 legs. The head count of the two species together is 12, and the leg count is 32. How many pigeons and how many rabbits are there in the zoo?

(A) 4, 8
(B) 6, 6
(C) 6, 8
(D) 8, 4
(E) 8, 6
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given
2x+4y=32
and x+y=12
solve for x , y
rabits = 4 and pigeons = 8
IMO D 8,4
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