nidhis.1408 wrote:A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability that both selected dogs are NOT littermates?
a. 1/6
b. 2/9
c. 5/6
d. 7/9
e. 8/9
Let's say that the 9 dogs are ABCDEFGHI.
6 dogs have exactly 1 littermate:
Let's say that A and B are littermates, C and D are littermates, and E and F are littermates.
This means:
A has 1 littermate (B).
B has 1 littermate (A).
C has 1 littermate (D).
D has 1 littermate (C).
E has 1 littermate (F).
F has 1 littermate (E).
3 dogs have exactly 2 littermates:
Let's say that G, H and I are all littermates of each other.
This means:
G has 2 littermates (H and I).
H has 2 littermates (G and I).
I has 2 littermates (G and H).
Total number of littermate pairs = 6:
AB, CD, EF, GH, GI, and HI.
Total number of pairs that can be formed from 9 dogs:
9C2 = 36.
P(littermate pair) = 6/36 = 1/6.
P(not a littermate pair) = 1 - 1/6 = 5/6.
The correct answer is
C.
If the GMAT were to use the word
littermate, a definition would be offered.
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