# Italian IMAT 2019 Q 59

Let R1 be the resistance equivalent to a connection of three equal resistances of value x, one of which is
connected in series with the other two connected in parallel; let R2 be the resistance equivalent to one
connection of three equal resistances of y value, one of which is connected in parallel with the other two
connected in series. What relationship must exist between x and y so that R1 = R2?
A) y = 4x / 9
B) x = 4y / 9
C) y = x
D) y = 3x / 2
E) x = 3y / 2

Hi everyone!
answer is B), i keep finding 3y/9… would love to see how someone else solve this one to compare

Hi!
Let’s follow as the question progresses.
R1= 3 resistors of value x of which two are in parallel combining with another resistor in series.
thus equivalent resistance for resistors in parallel will be x/2 and it will combine further with x under series combination giving us R1= x+ x/2=3x/2.

R2= three resistors with two in series combining with a parallel resistor.
equivalent resistance for the resistors in series=y+y=2y.
combining it with a resistor in parallel of resistance y we have R2= 2y x y/2y+y=2/3y.
for R1=R2
3x/2=2y/3
x=4y/9.
Hope it helps:)

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