Question

A number is divided into five parts. Twice the first
part, thrice the second part and four times the fourth
part are equal. Twice the second part, five times the
third part and six times the last part are equal. Which of
the following is always true if all the parts are integers?
(A) The first part is a multiple of 72.
(B) The second part is divisible by the fourth part.
(C) The first part is a factor of the last part.
(D) The product of the first and fourth parts is
divisible by 30.​

Answer 1

Answer:

only c is true.

Step-by-step explanation:

let 5 parts be a,b,c,d,e

from 1st statement, 2a = 3b = 4d

from 2nd statement, 2b = 5c = 6e

hence we can say 4a = 6b = 15c = 8d = 18e

dividing by 720,

we can say numbers r in ratio

90:60:24:45:20

a)The first part is a multiple of 72

false

b)The second part is divisible by the forth part

false

c)the product of the first and fourth parts is divisible by 30

true

d)the first part is a factor of the last part

false