Six numbers

[shashank.ism]

Six numbers a, b, c, d, e, f are such that a.b = 1, b.c =1/2, c.d = 6, d.e = 2, e.f =1/2. What is the value of (a.d : b.e : c.f) ?

A) 72 : 1 : 9
B) 8 : 9 : 9
C) 24 : 2 : 3
D) 6 : 1 : 9
E) 4 : 3 : 27

[lalmanistl]

My choice is A.

What is the right answer?

-Lalmani

[Cinji18]

Ditto. A.

[Stuart@KaplanGMAT]

Six numbers a, b, c, d, e, f are such that a.b = 1, b.c =1/2, c.d = 6, d.e = 2, e.f =1/2. What is the value of (a.d : b.e : c.f) ?

A) 72 : 1 : 9
B) 8 : 9 : 9
C) 24 : 2 : 3
D) 6 : 1 : 9
E) 4 : 3 : 27

You could set up all kinds of crazy ratios, but almost certainly the quickest/easiest way to solve is to pick numbers.

a*b = 1, so let's let:

a=1
b=1

Now working our way across:

1*c = 1/2
c = 1/2

(1/2)*d = 6
d = 12

12*e = 2
e = 1/6

(1/6)*f = 1/2
f = 3

Plugging our numbers into the question:

a*d = 12
b*e = 1/6
c*f = 3/2

Multiplying all three terms by 6 to eliminate fractions:

a*d : b*e : c*f = 72 : 1 : 9

Choose (A).

Here's the takeaway:

When you're given rules for how the variables behave, but no actual values, picking numbers that follow the rules is a great way to attack the question.

[shashank.ism]

Yeah the OA is A.
Let f = 1, then finding values subsequently,
e = 1/2, d = 4, c =3/2 , b = 1/3, a = 3
Value of ad : be : cf = 72 : 1 : 9