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12 Jul 2025, 06:13
Kudos
Bookmarks
F = number of falcons
H = number of hawks
O = number of owls
Owls = 1/3 more than hawks
So,
O=H+1/3H=4/3H
Hawks = 3/7 fewer than falcons
So,
H=F−3/7F=4/7F
Now plug value of HHH into OOO's formula:
O=4/3*4/7F=16/21F
Now total birds =
F+H+O=F+4/7F+16/21F
Let’s combine them:
F=21/21F
4/7F=12/21F
16/21F
Add them:
(21+12+16)/21F=49/21F
We want the smallest total, so we want the smallest value of F such that
49/21F
So FFF must be a multiple of 21.
Smallest such positive number = 21.
If F=21F = 21F=21
H=4/7*21=12
O=4/3*12=16
total =F+H+O=21+12+16=49
ANS 49
H = number of hawks
O = number of owls
Owls = 1/3 more than hawks
So,
O=H+1/3H=4/3H
Hawks = 3/7 fewer than falcons
So,
H=F−3/7F=4/7F
Now plug value of HHH into OOO's formula:
O=4/3*4/7F=16/21F
Now total birds =
F+H+O=F+4/7F+16/21F
Let’s combine them:
F=21/21F
4/7F=12/21F
16/21F
(21+12+16)/21F=49/21F
We want the smallest total, so we want the smallest value of F such that
49/21F
So FFF must be a multiple of 21.
Smallest such positive number = 21.
If F=21F = 21F=21
H=4/7*21=12
O=4/3*12=16
total =F+H+O=21+12+16=49
ANS 49
Bunuel
12 Jul 2025, 06:35
Kudos
Bookmarks
Lets assume number of falcons(F) to be 21
then number of hawks(H) will be
H = F - F3/7
H = 21- (21*3)/7 = 12.
and number of owls(O) will be
O = H + H/3
O = 12 + 12/3 = 9
Hence minimum will be 21:12:9
As ratio is already in simplest form
Sum of this ratio will be minimum number of birds, ie; 21 + 12 + 9 = 49
Hence option E.
then number of hawks(H) will be
H = F - F3/7
H = 21- (21*3)/7 = 12.
and number of owls(O) will be
O = H + H/3
O = 12 + 12/3 = 9
Hence minimum will be 21:12:9
As ratio is already in simplest form
Sum of this ratio will be minimum number of birds, ie; 21 + 12 + 9 = 49
Hence option E.
12 Jul 2025, 07:11
Kudos
Bookmarks
1/3 more owls than hawks: owls=hawks+hawks/3=4*hawks/3
3/7 fewer hawks than falcons: hawks=falcons-3*falcons/7=4*falcons/7
falcons=7*hawks/4
ratio is:
hawks:owls:falcons
1:4/3:7/4
Multiplying by 12 (3*4) to get integers:
12*1:12*4/3:12*7/4
12:16:21
The smallest possible total number of birds is:
12 + 16 + 21 = 49
Correct answer is E
3/7 fewer hawks than falcons: hawks=falcons-3*falcons/7=4*falcons/7
falcons=7*hawks/4
ratio is:
hawks:owls:falcons
1:4/3:7/4
Multiplying by 12 (3*4) to get integers:
12*1:12*4/3:12*7/4
12:16:21
The smallest possible total number of birds is:
12 + 16 + 21 = 49
Correct answer is E
