Question

A chain of car dealerships got a shipment of 9240 new cars there are the same number of cars in every color how many different colors could there be?
A)40
B)61
C)54
D)82​

Answer 1

B & D are perfect Squares as they have odd number of factors

Step-by-step explanation:

number of factor of A,B,C,D are 4,5,6,7 respectively

All perfect Square numbers have odd number of factors

B has 5 factors   - odd  number of factors

hence B is  a perfect square

D  had 7 Factors - odd number of Factors

Hence  D  is  a perfect Square

Examples :

1 is perfect square  - Factor  = 1    number of factors = 1   ( odd number)

4 is perfect square Factors = 1 , 2 , 4  number of factors =3  ( odd number)

9 is perfect square  Factors  = 1 , 3 , 9  number of factors =3  ( odd number)

16 is perfect square  Factors  = 1 ,2 , 4 , 8 ,16  number of factors =5  ( odd number)

non perfect Squares

6  Factors = 1 , 2 , 3 , 6  number of factors  = 4 ( even)

86  Factors = 1 , 2 , 4 , 8  number of factors  = 4 ( even)

12  Factors = 1 , 2 , 3 , 4 ,6  , 12 number of factors  = 6 ( even)

Hence B & D are perfect Squares as they have odd number of factors

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